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Issue 28 (July 2012)

1. Hg x i H E ILIK K O ty tz tz Q M Ux x XS JP a K x lt E RS Y v z SIK ps oe f tz ty ps ps l ps N O tz tz K K V ps Calculate and store the updated guess for the root T Did the solution converge Create a list containing the refined guess for the root and the X I iteration counter This list is the result of the function OST ND ee EXPORT GO Function that drives the root seeking program BEGIN ee Declare a local variable INPUT T Tolerance Toleran Prompt user with a form to enter the tolerance for the root Store ce Enter tolerance for he tolerance value in variable T root 1E 8 9 HE e eH H bo a Sa Me A E oO Q p a E YQ H INPUT X Initial Prompt user with a form to enter the initial guess for the root Guess Guess Enter Store the initial guess in variable X initial guess for the root 50 OST X T 2OLST Call function OST with the arguments X and T Store the resulting list in list variable LST MSGBOX Number of iterations Display the number of iterations in a message box Uses LST 2 expression LST 2 to obtain the number of iterations MSGBOX Root LST 1 Display the root in a message box Uses expression LST 1 to obtain the value for the refined root LST 1 Return the root END EDD UE i1 1n1dujhPl HP Solve 28 Page 10 Page 3 of 10 The code for function MYFX
2. As memory technology advanced the number of data registers increased with later models offering hundreds of data registers available to the user In some early HP models the use of data storage registers 1s shared by the calculator s functions The user must be aware of the ones that may have unexpected data in them and that they may even be cleared by the sharing usually statistical function s This article will review the storing and recalling of data feature found on HP calculators HP has been very creative in the way that data storage memory has been used Register sharing came first The second HP calculator the financial HP 80A9 followed the HP 35A 13 months later The scientific machine required the user to apply the formulas applicable to the broad fields of science and technology The financial calculator however had the many finance formulas needed in the business world built in This required 2 1 3 times the ROM memory Memory was very important but still technologically limited Several of the HP 80A statistics functions even used some of the stack registers for their use This made statistical function use a bit tedious The HP 80A single data register was called a constant storage location similar to the HP 35A At the time however the HP 80A was many times faster and more accurate than any other financial computational method available to the average user Unique storage features happened quickly The third
3. Coming soon 3005 Coming soon Both professors agree that the MCL is changing the way students learn and 35 TT comprehend complex math and science em x problems The MCL has become an A EA essential tool for mathematics education SERTHUNISE in China 39gii NEW 20 2J 40gs b g Visit www emcl org cn or www hp com calculators for more information HP Solve 28 Page 6 Page 2 of 2 Ostrowski s Method for Finding Roots HP Solve 28 page 7 Return to top Ostrowski s Method for Finding Roots Hamir Shammas Introduction Mathematicians statisticians engineers and scientists frequently deal with problems that require the calculation of one or more roots of functions When HP launched its first programmable calculator the HP 65 in 1974 the accompanying Standard Pac included a root seeking program The HP 65 Math Pac 1 also included another root finding program Over the following years HP released new programmable calculators each included root seeking programs in their standard and math pacs In 1978 HP launched the HP 34C that contained the very first built in root finding Solver The Solver was a new powerful and convenient tool for calculating the roots of single variable nonlinear equations The Solver implemented a clever version of the Secant method This method along with Newton s method remained the two favorite root seeking algorithms for many decades among users of prog
4. 12 See HP Solve Issue 16 The HP 41 system 30 years old for a detailed description of this most popular HP calculator that continues to be improved even as this is being written The HP 41 provided so many firsts that are explained in the article because it was a revolutionary leap in technology 13 One of the best sites for HP calculator usage all models in space is at hitp hpinspace wordpress com 14 Synthetic Programming SP is the use of HP 41 synthetically assembled instructions that cause the machine to perform illegal operations The PPC ROM User s Manual is the best place to start if you want to become familiar with the subject because SP is explained along with programs that will assist in the generation of the many synthetic instructions that are possible An example of this power is machine perfect Morse code I wrote an HP 41 program that was published in the PPC Calculator Journal February 1980 issue on page 50 Even using synesthetic tones the speed was limited to 6 words per minute A more sophisticated SP technique of addressing memory produces a speed of 16 words per minute A discussion of the technique to do this may be found in Keith Jarett s 1982 book HP 41 Synthetic Programming Made Easy page 151 The program in bar code is on page 163 HP Solve 28 Page 28 Page 10 of 10 Measuring Calculator Current HP Solve 28 page 29 Return to top Measuring Calculator Current Richard 0 Neleon
5. Issue 28 July 2012 HP Solve Calculating solutions powered by HP Issue 28 July 2012 Download the PDF version of articles Welcome to the twenty eighth edition of the HP Solve newsletter Learn calculation concepts get advice to help you Join our Facebook succeed in the office or the classroom and be the first to find Fan Page out about new HP calculating solutions and special offers In the spotlight Graduate to HP Calculators Don t get caught with a high school calculator in a college classroom Get your new HP 10bll or 50g graphing calculator during back to school season Read more Your articles The HP China Project HP has partnered with the China Ministry of Education to introduce graphing calculators and data collection technologies into high school math classes enhancing education Read more Store and Recall on HP Calculators Richard J Nelson Here is a historical review of how HP has managed the use of data registers and memory usage on their first decade of calculators the 70 s Many of these early methods are still in use today Learn more Is that calculator Answer Correct Richard J Nelson How do you know that the answer you have just calculated is correct A few easy to learn or review techniques may be applied to approximate the answer so that you could even get by without the use of a calculator if necessary Read more ite xA Urn
6. Efficiency 1s a vital part of the calculator s advantage in today s technical environment Calculator Usage Is Efficiency Important Notes 1 The calculation was for two parallel resistors which uses the product divided by the sum R FR The problem was evaluating an infinite ladder resistor network stage by stage 2 Keystroke counting is more effective if done to the nearest 1 2 keystroke Since each keystroke requires a search time and a press time there are situations where the same key is pressed twice This would only be l 1 2 keystrokes 3 You may further explore the issue of HP calculators in more detail by reading an article published for HHC 2006 The article is a dialog among six experienced users discussing the topic of Learning to Use HP Calculators See http hhuc us 2006 LearningToUseHPCalcs pdf HP Solve 28 Page 54 Page 3 of 3
7. Introduction The most important measurement of a semiconductor or semiconductor device is its current usage I once visited an assembly house in Asia that packaged integrated circuits IC s commonly called chips into plastic packages The finished IC s were then 100 tested using a massive computer controlled very expensive digital signal tester I noticed that the tester wasn t in use and I asked why The test engineer explained that they had found that they could simply measure the quiescent current and they could determine 99 9 of the time that the circuit was working Besides the hundreds and often thousands of specific digital conditions of the IC functions took much longer by a factor of at least ten Calculators are semiconductor products and measuring the current that they draw under various usage mode conditions provides a good indication of what is happening Pressing on with a blank calculator display just doesn t tell you very much Current 1s the most problematic basic electronics measurement vs voltage or resistance Modern digital nultimeters DMMs are cheap accurate and readily available All too often however you will find that the current range doesn t work usually because of a blown internal fuse Most electrical measurements are made by placing the probes across two points on the component or circuit under test Measuring current however requires that you insert the meter into the circuit This means tha
8. Keystroke counting is logically an efficiency measure for comparing calculators The use of the calculator however is by a human being and there is a human quality that may actually negate the fewer keystroke argument under special conditions If you repeat a sequence of key presses many times you may learn this sequence by rote If the sequence is five keystrokes and you are able to press these five keys faster than pressing a more efficient three keystroke sequence your skilled method may be more effective Dr Wickes HP s RPL Team leader used to ask this question How do you differentiate between familiar and friendly For the average user however using fewer keystrokes 1s better and more efficient Other efficiency issues Any comparison between two calculators that makes the machine easier to use could be considered an efficiency issue because the result is a savings of time Issues such as keyboard colors used display readability learning curve reliability keyboard layout and even accuracy all contribute to the calculator efficiency issue Conclusion The calculator continues to be important to users in spite of convergence because dedicated calculators are Inexpensive easy to use and efficient Efficiency is defined and how calculator efficiency may be compared with the most common contrary arguments explained Since efficiency is an objective measurement the conclusion that the answer to the title question has to be yes
9. L P The information contained herein is subject ta change without notice The only warranties for HP products and services are set forth in the express warranty sLatements accompanying such praducts and services Nothing herein should he construed as constituting an additional warranty HP shall nat be liable far technical or editorial errors ar omissions contained herein HP Solve 28 Page 3 Page of 1 The HP China Project HP Solve 28 page 4 Return to top HP Solve 28 Page 5 THE HP CHINA PROJECT Enhancing Education Through Strategic Partnerships In 2008 HP partnered with the China Ministry of Education to introduce graphing calculators and data collection technologies into high school mathematics classes as an effort to enhance student comprehension of mathematic principles Guided by the training and academic research of Professors Wang and Cao from Beijing Normal University over 120 pilot schools in 15 Provinces throughout China are now using HP 39gs graphing calculators and the HP Mobile Calculating Lab MCL Wang and Cao determined through their research that the key goals of mathematics education are to further develop Educators improve course curriculum content and evolve Chinese teaching models to focus on multiple representations of mathematical expressions and open ended problem solving The HP 39gs graphing calculator enhances mathematical understanding by allowing students to easily toggle between n
10. but without a crystal or HP documented means to access the code Many users installed their own quartz crystal to have their own HP 55A timer The HP 55A did not have register arithmetic and program memory was limited to 50 lines instructions The number of data registers however more than doubled from 9 to 20 what was previously available The registers were addressed as RO R9 and R O Fig 7 HP 55A R 9 The method of using zero and the decimal point retained the by then well known method of addressing data registers This provided the lowest keystroke count implementation that HP is so well known for Even more data registers The next programmable scientific calculator the HP 67A added 6 additional storage registers and a new scheme that changed how they were used Keystroke efficiency must have been strongly considered as shown in Fig 9 The top row of five keys were identified A E Associated with these keys were five primary data registers plus a 6 T register See Fig 8 below A second 10 registers were called secondary registers RO R9 If you wanted to store N into register A you put N in the X register and pressed STO A e g N STO A The I register required a shift STO If you wanted to store the number into a secondary register you pressed N STO 0 In this way 16 registers A E I amp RO R9 could have values stored and recalled by pressing two keys A second set of ten
11. flowing and turning all conductors cherry red There are several reasons The wiring involved may be HP Solve 28 Page 30 Page of 6 very small resistance of the wire may limit the amount of current that will flow The power source may have a built in resistance that may limit the amount of current that will flow Calculators are usually battery powered and the internal resistance of the physically small battery will usually limit the current This source resistance is what the calculator electronics sees When you insert your current meter into the circuit between the battery and the calculator the calculator will see the meter resistance and the battery resistance in series Both the meter and the battery will have its source resistance dependent on the conditions at the moment The battery source resistance will be quite low when it 1s first used The internal resistance will slowly increase as the battery supplies energy and it will be quite high at the end of life The meter resistance will change when the range 1s changed A high current range will have a much lower resistance than the low current range Digital Circuits are Time Sensitive We have all heard that digital circuits are very fast Most human activities such as key press times reaction times or neural response times are measured in the low millisecond range Digital circuits respond a million times faster and the circuits that interface to the human world mu
12. 2 ev pe imde Hyster gt i s Serial Port s pins _ 82153A Wand Phineas iR Infra Red LR SEE ext 1 0 ou vO Not shown 3 x n 82143A 9 79 82184A Q BASICLanguage OS Peripheral Printer Plotter 41 65 67 97 Helios 14888 E CAS Mag Cards X Ee Aviation RPN Algebraic Sii e 14023 iiri 2 go ooo HESES RPN unless indicated Grapenuts Fig 4 Example of Table 1 Accessories and Miscellaneous categories Fig 5 I O and OS Legend One calculator is not shown but is mentioned the HP 97S with its special I O A special frequency modulation printing process makes this poster of exceptional quality While this description 1s quite complete there are still discoveries to be made by studying the poster UE The poster cost is 19 95 plus 5 05 for shipping One poster with shipping is 25 00 Shipping is by USPS Priority in the US and Airmail postage to Canada or Mexico See the website for shipping to other countries The poster makes a unique gift for any HP Calculator collector 7 77 E itti http www vcalc net hp htm Cricket mI HP 01 9 Silver Rick also has a few other unique posters See his website for the details His order MA Aen i Fig 5 The only processing is first class and his shipping is speedy on receipt of order Special pricing ingsesu au and reduced shipping is obtained for multiple poster orders readable legends A Bit of HP History PH or HP Every now and the
13. Conference coverage Issue 26 January 2012 pp 10 amp 12 The WP 34S Evolves by Jake Schwartz Issue 27 April 2012 page 34 ee he If you need a WP 34S Overlay http commerce hpcalc org overlay php This page will also provide the written instructions on how to flash the calculator as well as how to obtain a WP 34S machine Here is the content of this issue S01 Graduation Calculators Summer is a time for finishing one phase of academic life and moving to a higher phase HP calculators for this forward move are featured S02 The China Project There are a lot of students in China that need HP calculators Here is a report on how HP 1s working with the China Ministry of Education to introduce graphing calculators and data collection technologies to these students S03 Ostrowski s Method for Finding Roots by Namir Shammas explores an improved Newton s method for finding roots that all students learn in school The Ostrowski method is examined explained and exampled with programs for the HP 39gII and the repurposed HP 30b aka WP 34s Here are typical examples x x exp x sin x 3cos x 5 x sin x x 2 X cos x X x sin x x 1 f x exp x cos x HP Solve 28 Page 44 Page 1 of 7 S04 Store and Recall on HP Calculators the First Decade Calculator memory always seems limited because as improved technology provides additional memory more complex problems become calcula
14. FIX DSE GTO including storage arithmetic and flags The HP 41 has two flags that may detect data entry an ALPHA input flag 23 and a numeric input flag 22 HP Solve 28 Page 26 Page 8 of 10 summary observations and conclusions Most calculators have the feature of providing one or more storage registers for storing numbers for use during a calculation or for future use sums constants etc This article 1s a review of the use of data registers of the calculators HP made during the first decade of their calculators the 70 s Business and scientific calculator applications may require a surprising number of data registers and the calculators of this period ranged from one to 319 registers In most cases these data registers are shared with the user by statistical functions that usually need six registers and the stack when they are used In addition to function sharing many HP calculators have a feature of performing storage and in some cases recall arithmetic in the data registers In more advanced machines such as the HP 41 register arithmetic 1s allowed in the stack as well Because the HP 41 is an alphanumeric machine alpha characters as well as data may be stored in data registers Programmable calculators often have a memory tradeoff feature wherein program memory may be used for data storage In all cases HP has designed their data register usage to be as keystroke efficient as possible Store and Recall on HP Calculato
15. Fig 1 Most straight forward programming method stores variables and recalls them as needed 9 steps My second program utilized the LASTX register in order to save a register because most calculators work faster 1f the calculations are done on the stack See Fig 2 below This saved one program step Step 1 2 3 4 5 6 7 8 9 T P Bud T ad T Y Pal Pd ae Z v AXB Y A A B AXB A AxB X B B A AXB A B A B AxB A B AxB A B press START STO Xey x LASTX RCLI 5 R S Fig 2 Improved program using LASTX to avoid using a storage register 6 steps saves one step The third and final program uses the stack for all calculations by using the R7 operator and auto T register replication LASTX is considered part of the stack See Fig 3 below This program uses nine program steps Step 1 2 3 4 5 6 7 8 9 10 i a A B B B B B B B oa A B B B B AXB B B B Y A B B B B AxB A AB B B X B B B A AXB A B A B AxB A B AxB A B press START 4 f RT x LASTX Rt E R S Fig 3 Program variation to make all calculations on the stack for maximum speed 9 program steps HP Solve 28 Page 53 Page 2 of 3 Note that all programs end with Run Stop R S so that the R S key 1s all that is needed to run the program This works because it was the only program in memory I concluded that the Fig 3 program is the most efficient way to use the machine for making these calculations under these conditions Efficiency vs skill
16. RCL related keys The First finance E series machines was the HP 37E It has seven data registers RO R6 The previously four mentioned E machines were simple and non programmable The remaining four machines are more powerful and have more memory Data memory shared with program memory The HP 38E business calculator was HP s first programmable business calculator introduced 5 1 78 With up to 99 lines of program memory it also shared statistical registers R1 R6 The default Automatic Memory Storage memory allocation 1s eight lines of program memory Stack Registers and 20 storage registers Each additional program Fig I4 HP s lowest cost 1978 scientific the HP 31E line consumes part of a data register starting with T BOO COE Ro BEXPSERSSSNS RS 7 a CLC Each data register provide an additional seven lines Y fo gooo Re BERE ES n of program See Fig 16 and 17 for the HP 38E Display R3 RA Om 2X memory register allocations When you add the ninth y ENZIIEENENNM n BEC CES Yx program line memory is automatically taken from the y last data register R 9 While this may seem strange LAST X Hs ccc RUN y based on today s machines it 1s important to keep in BORIDDEERENNS Rs eO 16 es dy mind that this was the state of the art in mid 1978 R ROTIE EAE Sxy 7 As shown in Fig 15 the display was still power an hungry LED s and the batteries were rechargeable Fig 15 HP 33E register designations NiCad s
17. data registers are the primary storage registers ROO R99 The STO and RCL operations require two digits The display prompts for the register number with two underscore characters The HP 41 has a register clear CLRG function Storage register arithmetic may be applied to the primary data registers ROO R99 Storage register arithmetic may be performed on the stack as well The HP 41 will also provide a register overflow message OUT OF RANGE A nice additional feature of the HP 41 is the ability to ignore error messages under the control flag setting of the user Data registers are used by the HP 41 for statistics functions The normal six registers however are not fixed in that the user may set the starting register with the X REG function The HP 41 keeps track of where these are and a CL function will clear these six registers The HP 41 will use any register as an indirect addressing register with an IND function When the sequence STO IND is executed the display will prompt with STO IND The user then provides the register number or alpha designation of the register to use for the register address If you have SIZEd your machine to have more than 99 data registers you must address them indirectly 1 e three digit numbers R100 R318 The alpha and stack registers may also be addressed indirectly While not relevant to the data registers the HP 41 may also take numerical arguments for certain functions indirectly e g TONE
18. in place as the battery pack 1s slid in The internal battery change capacitor used for the HP 41 is large enough that it will retain a program in memory for many hours often overnight Because of this you may have to reset the machine by placing a jumper across the two outside battery compartment bumps and holding it there for at least 15 seconds A calculator latch up may occur when you change current ranges on simple DMM s Here are some very simple measurements of an HP 41C to illustrate OFF 0 5 uA ON 0 53 mA Loop 4 19 4 22 mA Pressing Key 4 13 mA Loop 4 26 mA HP Solve 28 Page 32 Page 3 of 6 Notes 1 The value slowly drifts down to 0 1 uA which is the lowest resolution of the 3 Harbor Freight sale DMM Comparing this DMM to a laboratory standard shows that it 1s quite accurate 2 In Fix 4 display 3 Using a simple LBL 01 BEEP GTO 01 loop 4 Any pressed key draws about the same value 5 Using a digit entry loop LBL 03 123456789 GTO 03 If you duplicate the measurements using the same meter you will notice that the calculator won t turn on 1f the selected range is left on the lowest range 200 uA Use two switch positions higher in the 20 mA position of the rotary switch If you want to avoid the meter switch range changing issue you may measure the current by measuring the voltage drop across a resistor inserted between the battery and the calculator This i
19. is simple and requires a single statement for the tested function The function MYFX has the parameter X to pass the value needed to calculate the mathematical function f x The code for the function OST has the parameters X and T which pass the values for the initial guess for the root and the tolerance respectively Notice the following aspects about this function The LOCAL statement that declares a number of local variables that have multi character names The REPEAT UNTIL loop that implements the iterations needed to refine the guess for the root The UNTIL clause tests the convergence criterion The test determines if the absolute difference between the old guess for the root and the new one falls at or below the tolerance value The function s return value which is the list X I This list contains the refined root value X and the number of iterations I The code for the parameter less function GO has the following three parts Two INPUT statements that display input forms to obtain the values for the tolerance and the initial guess for the root A call to function OST The function GO stores the result of OST in the local list variable LST Two MSGBOX statements to display message boxes showing the number of iterations and the refined guess for the root The function uses the expression LST 1 and LST 2 to access the root value and number of iterations respectively The function GO returns the refined root value This ap
20. register arithmetic A number outside the range of 0 29 stored Re Ris in RO will error if the indirect function is performed E Ries o 26 The decimal part of the RO register number is ignored and it may be negative R Ron for rapid reverse branching in a program The HP29C also has a register clear Rez Roe function Rs Pon Different storage registers The first HP 10 7 1 77 is a one of a kind printing calculator obviously intended as an office calculator and is neither a business nor scientific calculator It has two storage registers The Accumulator and Memory Per the Owner s Handbook Basically the accumulator is a memory that holds numbers while you perform other calculations The Accumulator is associated with the double high blue key see Fig 12 and accumulates values as numbers are added or subtracted This key is typical of adding type machines The HP 10A Memory is described as a holding bin or storage place for numbers The complete keyboard is shown at the right in Fig 12 Note the three M keys in the top row Note that the gold shift key only has three functions associated with it Less data memory for a lower cost Fig 12 Complete HP 10A Keyboard The last two years of the first decade 70 s of HP calculators brought us the Spice Spike series of calculators These machines are also called the E series because the first five models had an E suffix Two of the three remaining models
21. scientific notation with exponents subtracts the exponents Divide 4723 by 13 46 5E3 IEI 5E2 or 500 E3 E1 E2 The calculator gives HP Solve ft 28 Page 38 Page 2 of 3 350 8915300 The approximate answer may seem a bit low and here is where experience and judgment may be applied in terms of how you round the numbers The denominator 1s much smaller than the rounded value and the estimated result is expected to be larger Making a Guess Leads to the Exact There are many methods and techniques for making numerical calculations and professionals who work with calculations will learn a few of them such as the rule of nines Books have been written on the use of the rule of nines in accounting validating numerical calculations Suppose you needed to know the average of the following numbers these were measured values Value 106 4 2 108 2 3 109 4 110 Guess 5 lll WN 6 110 0 You first make a guess by examining the numbers In this case the guess is 110 Next you note the differences between your guess and the values The third step is strike out the values that cancel This leaves a total of 6 There are six values so the average error of the guess is 1 110 1 is 109 The average value 1s 109 exactly Conclusion Experience in problem solving provides a sense of what the answer should be The student doesn t have that experience and he or she should develop techniques or methods to provide an approximatio
22. secondary registers Rs0 Rs9 are protected and shared with F6 HP67A Keys other calculator functions A special function ES exchanged the contents of the two sets of secondary registers The STO and RCL keys would operate as they did normally Fig 9 below shows how all the data registers are designated The T register is a special indirect addressing register that is also shared between the user and the HP Solve 28 Page 21 Page 3 of 10 machine A related STO amp RCL calculator function T Primary is a register review feature introduced in the HP Z Registers 67 97 calculators iC R Another feature related to the SRO RCL functions is X R the clear register function This function clears all iy INCUN Protected of the primary data registers To clear the secondary AeT x Cd R Secondary registers the BBJ key is pressed and the clear Registers register function executed again REC 1 Re 777 R Asef Another advantage the HP 67A offered over the HP iy 1 iy 65A 1s that the data registers were recorded onto a R Re magnetic card RL Rl S J Re From the above description it should be clear that HP 67 97A SL Re keeping track of which register values are in the RO M a E R9 primary vs secondary registers 1s up to the user Fig 9 Data register designations of the HP 67 97A One register six keys The STO and RCL features of the seven machines described ab
23. Continuous memory arrives at the end of the E series 7 1 79 The HP 33C is identical to the HP 33E except that program and memory do not disappear when the power is turned off The HP 38C is identical to the HP 38E The big news of the E series was the scientific HP 34C This was a new machine and it didn t have an E predecessor Memory was a minimum of 70 program lines and a maximum of 210 program lines when the 20 data registers are similarly used as shown in Fig 17 The major contribution for the HP 34C HP Solve 28 Page 24 Page 6 of 10 Program Storage Registers Program Storage Memory Registers wo R R o 00 ul a Rm R L it 4 2 fab afi e n se aea R C ow RE mE Reo REC GJ RE 03 R oS a C RL RLO Boo ipu Bab ed amp m amp L we Fig 16 HP 38E register allocation 1 reg 7 prog lines Fig 17 Additional prgm lines consume data reg was the new and extremely powerful applications of Solve and Integrate Continuous Memory was a technology advancement that once started made it obvious that all HP calculators would soon be made using the CMOS process that needed such a low power that the machine is really never turned off CMOS memory and HP 41 changes everything 1979 was a milestone year for HP calculators because of a new calculator concept represented by the HP 41C CV CX The HP 41U utilized CMOS memory and it used an alphanumeric LCD display It
24. D coded for the following function f x x 10 In 1 Ax 2x Let s run the program to calculate the root with the initial guess of 50 and a tolerance value of 1E 8 The root is approximately 223 226 To run the program perform the following steps 1 Execute the command XEQ OST to start and initialize the program To rerun the program simply press the key A 2 The program prompts you for the tolerance value as shown in Figure 6 The display shows the current tolerance value of 0 00000001 This is the initial value set by the program in step 1 If you enter a different value and rerun the program you will see your most recent tolerance value In the case of our example accept the current tolerance value and press the R S key HP Solve 28 Page 15 Page 8 of 10 TOLER oz AN Y N A N A I A IR A A A a A E E Fig 6 The prompt for the tolerance value 3 The program prompts you to enter the initial guess for the root as shown in Figure 7 The value in the X register is a leftover from step 2 Just ignore it Enter the value of 50 and then press the R S key GIESE seo ar wigininininioion AN A A O A A A A A Gg Fig 7 The prompt for the initial guess for the root 4 The program pauses to display the series of improved guesses for the root When it finds a refined root guess that is within the tolerance you specified it displays the number of iterations as shown in Figure 8 The figure shows how the alpha and X r
25. HP calculator the scientific HP 45A followed the HP 80A three months later 5 1 73 The number of storage registers increased to nine and the STO RCL operations increased in their capability These three machines are classical RPN calculators The STO and RCL operations however were not RPN in the way that the machine used them RPN is postscript logic wherein you provide the data followed by the operation Storing a number e g 7 in Register 1 should have the RPN sequence 7 1 STO Instead the sequence is 7 STO 1 This 1s explained by the inventor of HP calculators Tom Performing Register Arithmetic Arithmetic operations xX can be performed between a Osborne Tom explained this during an interview of the data storage register and the X register display To modify the con HP 35A development team during a special event at HP tents of the storage register press sro followed by the applicable op Labs when the IEEE presented A plaque honoring HP on erator key X then the number key specifying the storage register For example store 6 in register R then increment May 14 2009 See HP Solve Issue 14 RPN Tip 4149 7575 near the end of the article I probably would have used Press See displayed postfix on store if we had more than 10 storage cells 0 6 sro 1 EH 9 but STO N seemed much more easily understood 2 B8 88 1 MINE 2k than N STO Howeve
26. MMMgzaaaakaksesescss sebkhNW sTO 01 ROI x RCO pope a a Ich 88 1 NEHME the slope at x as f x h f x h RCL 01 J STOOL Calculate Ces s PS o f xy f x a SRO i cg sd STO0 s RCL 02 pReL00 DL 2 J 0 JJ J REL01 9 L Eoo m o Eo o x0 IN TO ao ooo Eoo ool 0o j 0 J RCLOS O x J RCb04 45 Re 4 JSTOX PopLR Remove local registers PP EN aa a LBL A _ Labelusedto rerun the program RCL O1 0000000000000 E CC LN p D new text Lu MN JCalculate y f y x yy f x 2 f y TER rar 00 ett RCL 05 Push current tolerance value in the stack PROMPT Prompt forthe tolerance value STO O0 Storenewx 0 0 sto0s Cd HP Solve 28 Page 13 Page 6 of 10 Program Step Comment Program Step Comment LBL B Label used to simply enter a new guess for the root xx pewx oldx tolerance C Clear the alpha register to start building new text INC 06 Increment iteration counter RCL 06 C Clear the alpha register to start RCL 05 building new text PROMPT Prompt user to enter the guess for the Resume iterations root a Initialize the loop counter a La RCLOO PROMPT Display the number of iterations Display intermediate guess for the C Clear the alpha re
27. P 39G HP 40G 3 tt R 1 5 3 PR ae Bondi Hammer amp s Alcuin RS plus As E v5 Enterprise Enterprise Darsan 02 811654 1902 GPIO Ieterface Foamut BILOBA 1933 ul e x at 2 28 z 3 TT rr rrr Tee MS Sneak eeanannaae I oO Mose a anaes ee Ssacaneana s nc Si enoseoccm 5 3 2 82240B ECET TP a pa HP 19B HP 19BII IR Printer 5 93 Tycoon Tycoon II lst ne Desktop 100A 8 1968 High e Oesktops 8104 1971 8204 1972 amp IOA 1972 5954 1973 58154 1976 98155 1980 8254 1975 Printing Desktoos Hf 45 5 73 A HP amp 1 5 73 oe SSW JI HP 2001X Lion Qum aye ean a2 aae eac852 oc OR Ge eae 22 ee oo oe PIONEER s SD lt D THE CALCULATORS or pJ HEWLETT HP 325 Leonardo HP 17BI eet chown Trader I 3 95 HP 1000CK Puma 2 97 5 91 gH Ig g HP 3251I HP 325II g I Nardo E Nardo ui Vinea qu P4 nar bl a X EJ 4 97 THEY m 2 c t 5 lt G3 LCS ES EE EJ j Se Bo E T m JE E en t 3 9 E Cy L2 Em rj o 5 nunahubana b a 9 o a Z a Vau ua aa ea on o o a e D 32 oF noom cm oe oe Ce me oe oe c 2 HP 305 4 HP 10BII 5 Ene we og Ua HEE RIDE v Astro Ago R202 R s Trader 3 m V HP 48gll 2 HP 39g amp 2 MP 39gs M Mid Apple LittleAppl
28. Peer ie du HIP A D Aged Mri a Lt modd Serene sm ce haa Lim rar dT sion Wri is 2 ila p ml prir hen nem Bl ee D IZ eet Be abd Eik p iai baa a ai A HT Tak rreri Laure From the Editor Learn more about current articles and feedback from the latest Solve newsletter including a new One Minute Marvels and HP user community news Learn more Update profile Change email Contact the editor Ostrowski s Method for Finding Roots Namir Shammas Namir explores an improved Newton s method for finding roots that all students learn in school The Ostrowski method is examined explained and exampled with programs for the HP 39gll and the repurposed HP 30b Read more Measuring Calculator Current Richard J Nelson You press the ON key and nothing happens now what You replace the batteries and still have a blank display do you throw it out and buy a new one The most powerful technique to knowing what is or is not going on in your calculator is to monitor the current it draws Learn more Calculators and Prefix Units Richard J Nelson Calculators must be easy to use Here is an idea for making them even easier and more convenient for problem solving What do you think of this idea Read more Calculator Usage Is Efficiency Important Richard J Nelson One of the reasons why calculators are still popular is their efficiency This article reviews what this means and dispels so
29. address below Calculators and Prefix Units Note 1 Twenty one decades of prefix values is represented by the frequencies of the Electromagnetic Radio Frequency Spectrum The internationally allocated RF frequency is between 9 KHZ 10 and 300 GHz 10 and the known frequency range is 0 to 3000 EHz 10 This includes IR visible light uv and X rays Tera is 10 Penta is 10 Exa is 10 About the Author A Richard J Nelson a long time HP Calculator enthusiast was editor and publisher of HP 65 Notes The PPC Journal The PPC Calculator Journal and the CHHU Chronicle He has also had articles published in HP65 Key Note and HP Key Notes As an Electronics Engineer turned technical writer Richard has published hundreds of articles discussing all aspects of HP Calculators His work may be found on the Internet and the HCC websites at hhuc us He proposed and published the PPC ROM and actively contributed to the UK HPCC book RCL 20 His primary calculator interest 1s the User Interface Richard may be reached at rjnelsoncf a cox net HP Solve 28 Page 42 Page 2 of 2 From The Editor HP Solve 28 page 43 Return to top From The Editor Issue 28 summer is in full force here in the Arizona Sonoran Desert of the Valley of the Sun with triple digit temperatures during the day and high 80 s at night While most people get outside during the summer we do not because the heat here can kill you The repurpos
30. as the HP 19C which was a small desk top machine with thermo printer The HP 29C was the first machine of the last RPN Stack list logic change as described in Table 1 on page 42 of HP Solve issue 27 9 HP has used the 10 model number more than any other number Examples are HP 10A HP 10B HP 10 BI HP IODbII HP IOBII HP 10C HP 10s and HP 10 Quick Calc The space in Quick Calc is shown on the machine and was not actually intended as represented in the named models that followed The HP calculator collector would have more than these eight models because of color variations sold with the same model number For detailed information on the sharing of model numbers see HP Solve issue 20 page 25 The A suffix is added here to indicate it is the first HP 10 http h2033 1 www2 hp com hpsub downloads Newsletters_ HP Calculator eNL 08 August 2010 pdf 10 The cost in 2012 is based on the Federal Reserve Bank of Minneapolis consumer price index cpi calculator at http www minneapolisfed org 11 Every HHC 2010 attendee received a copy of this booklet with their conference proceedings because it a rare tutorial on Classical RPN The manual printing cost was kept low by having the majority of the pages of the E series manuals in the 56 page Solving Problems with Your Hewlett Packard Calculator which could be printed in larger quantities The specific details of each model were in the much fewer pages individual model manuals
31. at the article will encourage you to use the efficient Ostrowski s method in future programs that you write References 1 A M Ostrowski Solution of Equations and Systems of Equations Academic Press second edition 1966 2 Walter Gautschi Alexander M Ostrowski 1893 1986 His life work and students can be downloaded from http www cs purdue edu homes wxg AMOengl pdf 3 Walter Gautschi Numerical Analysis Birkhauser Boston 2nd ed 2012 edition December 6 2011 4 W Kahan Personal Calculator Has Key to Solve Any Equation f X 0 Hewlett Packard Journal December 1979 5 F Soleymani and M Sharifi A New Derivative Free Quasi Secant Algorithm For Solving Non Linear Equations World Academy of Science Engineering and Technology 55 2009 6 Xia Wang and Liping Liu New eighth order iterative methods for solving nonlinear equations Journal of Computational and Applied Mathematics 234 2010 1611 1620 7 Reza Ezzati and Elham Azadegan A simple iterative method with fifth order convergence by using Potra and Pt k s method Mathematical Sciences Vol 3 No 2 2009 191 200 8 Guofeng Zhang Yuxin Zhang and Hengfei Ding New family of eighth order methods for nonlinear equation COMPEL volume 28 issue 6 2009 9 M Heydari S M Hosseini and G B Loghmani ON TWO NEW FAMILIES OF ITERATIVE METHODS FOR SOLVING NONLINEAR EQUATIONS WITH OPTIMAL ORDER Applicable Analysis and Discrete Mathemat
32. c func tions and polar rectangular conversions any values stored there will be lost Otherwise register R may be used for general purpose storage were not completely without restrictions R5 R9 were shared by other calculator functions See Fig 3 text from the Owner s Handbook OH for the details in the same manner as registers R R 26 Fig 3 HP 45A OH Restricted Storage description Recall arithmetic applied as well The HP 45A Owner s Handbook explains Conversely to alter the X Register displayed value without affecting the contents of the data storage register or the other stack registers press RCL the applicable operator then the number key specifying the storage register The statistical registers may be also be used as summing registers R7 yx amp R8 yy Using the gt key to store the sums of two numbers at the same time is very keystroke efficient without using register arithmetic The next major advancement in HP calculators was to add programming with the introduction of the HP 65A on January 1 1974 This machine caused an explosion of HP calculator user activity Memory was still relatively expensive and the HP 654A like the HP 45A had nine data registers R1 R9 Fig 4 at the right provides the HP 65A Owner s Handbook details of the usage of the nine data registers on pages 29 amp 30 The HP 65A was programmable with enough memory for 100 program instructions and it 1s poss
33. cond step inserts the last three characters ER The WP34S displays the character a to the left of the inserted text You can insert one character per program step but that is both wasteful and makes the listing harder to read While entering letters in the alpha register is easy entering the space the question mark the equal sign and other punctuation characters requires some practice The WP34S calculator stores various non alpha characters in different menus and key combinations I would like to point out that you can also append numbers to the alpha register This feature which I chose not to use in this article can help to prompt program users in the input and display of array and matrix elements 5 The program uses the INC command to increment the value of a memory and also stack register by one The above listing uses the command INC 06 to increment memory register 06 that stores the iteration counter The WP34S has the DEC command to similarly decrement the value of a register by one The INC and DEC commands are very handy in directly adding or subtracting 1 from a memory or a stack register without pushing 1 into the stack This direct action does not disturb the stack When all of the stack s contents are relevant using INC or DEC is a welcome feature 6 The PSE n command pauses the program for a specified number of tenths of a second The above listing uses the command PSE 10 to pause for one second The above listing has LBL
34. d reference points to a recently published book written by him Ialso included references to several articles I found on the Internet which present variants for the Ostrowski s method I encourage you to search for these articles and learn more about these new algorithms The HP 39eII Listing Table 1 contains the commented listing for the HP 39GII calculator The table shows the following functions e The function MYFX which implements the code for calculating the mathematical function f x e The function OST which performs the calculations for the Ostrowski method This function makes several calls to function MYFX e The function GO which uses forms and message boxes to interact with the user This function also calls function OST to obtain the number of iterations and the root value HP Solve 28 Page 9 Page 2 of 10 Table 1 The HP 39eII Listing Statement Comment EXPORT MYFX X Define function for f x 0 BEGIN X 10 LN 1 4 X2 2 X 4 END 7 77 T a SEEMMMEMMMggJ EXPORT OST X T Define the function for the Ostrowski method The parameter X is the initial guess for the root The parameter T 1s the tolerance value BEGIN Se S 031 x3x0 0 001 ABS X 1 OH Calculate and store the increment h used to numerical evaluate the derivative H FX MYFX X H FX DDIFF Calculate and store the refinement for the guess DIFF Y Calculate and store the value for y Calculate and store the value for f y
35. del has raised teacher expectations of students and students have met the challenge by responding with creativity and advanced reasoning This new found approach to the teaching and learning of mathematics is quickly taking hold in communities throughout China To offer ongoing support HP sends experts from an international community of math teachers to gather at summer and winter camps in China to share ideas resources and pedagogy One of the key highlights of these camps is the young scholar s math competition which provides students greater opportunities to develop high level insight to difficult concepts such as mathematical programming The HP China project has allowed for excellent research the building of solid teaching pedagogy student motivation and understanding of mathematics and it has provided many educators with a newfound method of teaching Professor C P Wang ATCM 16 Bolu Turkey 2011 Earlier this year HP introduced the ft 39a l newest member of its graphing Tsat o calculator fa mily the 39g Il HEINE coor Hy ERE This new calculator maintains HEHN HP s iconic plot numeric and EREBEREE AREE F3 S ESESEESEE symbolic keys to facilitate easy HEAT EA EEE toggling between mathematical representations Chinese characters and full Chinese menus have also been added to comply with the China MOE requirements Scientific HB OB le v 23 zm z3 72 53 93 9 Mem D EB PA EE 10s
36. e Z o o HP 12c Platinum 3 HP i2 Prestige HP 12c Platinum I T 1 1 1 1 3 Us 12d pt o seld in Breet amp s 25th Anniversary gsm m StreamSmart 400 7 mm Datastreamer gt ge um nwa omia m ever OO aro a Uo CIO Ue insani dene Ed DBR RUKI enoa enc aeuum wit 1 08 HP 1O0bII 3 HP 17bII Fi R2D3 a Retro Trader a 1 seg as x 7 wf 2 HP 3s HE HP 10s 37 o a China Scientific 5 Bs Solar a iPhone Apps ZAHP 15C Limited Edition z HP 12C 3 HP 40q HP 39gII s HP 15C I i15C orCedar 30th Anniversary Ed amp Littie Appia I Aswan HP 12C rp HP 12CP 30 Kaperposcobis inv rm wna 9 50 meram HP 10 Quick Calc 3 xm colon green pri s rer bronze calcPad 200 1 e EP OfficeCalc 300 i The Calculator Reference www vcalc net v5 22 Rick Furr May 15 2012 2 CalcPad 100 2 Copyright 2004 2012 gt HpCALCS 200 5 12204009 pet c gt ZHP 10bIIs R2D4 EasyCalc 7 100 PrintCalc 100 ex G OfficeCalc 100 i HP 300s l SmartCalc Z 8 OfficeCale 200 z 3 10 08 HP Solve 28 Page 48 Page 5 of 7 82106A Memory Module R Repurposeable ARM UO 82170A i 2 9 e eni USB Micro 5B B2180A USB Mini 55 S Extended Funct 69 StreamSmart 82181A Serial Port Micro 4B 82104A Card Rdr Wil
37. ectronic values are similar 0 01 Amperes is immediately converted to 10 mA by those who use these values The usage of milliamperes even extends to thousands Battery cell capacity may be rated at 1200 mAh rather than 1 2Ah These examples illustrate that in practice engineering units are not always in multiples of 3 as indicated by the unit prefixes Kilo or milli I like the mm vs cm example to illustrate that the purpose of the calculator is to make the task easy and simple I know that 1 8 cm is 18 mm This is a no brainer but when I have my mind wrapped around a problem I find it easier to not have to mentally move that decimal point I know that 1 2Ah is 1200mAh but I don t want to make that mental conversion if I don t have to because my focus is on other things The need for the conversion is that all the other similar values from data sheets etc are expressed in mAh rather than Ah They are equivalent and are only expressed using different prefix values HP Solve 28 Page 41 Page 1 of 2 Many programs program libraries have been written to make electronics related calculations Resistance values are more common above the basic unit of 1 ohm Capacitor values are quite different because the unit value is the Farad and 99 of capacitor values are a very small fraction of a Farad Capacitor values are most commonly in microfarads nanofarads or picofarads Current values Amperes probably have the greatest range and cur
38. ed When H P did enter the calculator market it did not compete with existing manufacturers it created a completely new market the scientific calculator market References 1 The HP 35 A Tale of Teamwork with Vendors by Gerald M Walker Electronics February 1 1973 2 Hewlett Packard Company Annual Report 1973 3 A New Electronic Calculator with Computer Like Capabilities by Richard E Monnier About the Editor Richard J Nelson a long time HP Calculator enthusiast was editor and publisher of HP 65 Notes The PPC Journal The PPC Calculator Journal and the CHHU Chronicle He has also had articles published in HP65 Key Note and HP Key Notes As an Electronics Engineer turned technical writer Richard has published hundreds of articles discussing all aspects of HP Ge Q Calculators His work may be found on the Internet and the HCC websites at hhuc us He proposed and published the PPC ROM and actively wea contributed to the UK HPCC book RCL 20 His primary calculator interest E is the User Interface Richard may be reached at rjnelsoncf cox net HP Solve 28 Page 50 Page 7 of 7 Calculator Usage Is Efficiency Important HP Solve 28 page 51 Return to top Calculator Usage Is Efficiency Important Richard Y Melson Introduction In recent years the usage of or need for a calculator has been questioned Students are required to have a computational tool and business users need special business appl
39. ed HP 30b aka WP 34S is an RPN scientific calculator creation the HP user community uses to explore new ideas for the high machine The HP 20b is also repurposeable but it has been phased out so the 30b is the primary machine to reprogram Of course the HP warranty is voided Once the experimental user makes this step into the unknown it is usually a go for broke move that is exciting educational and often inspirational Many users have now added a low cost IR diode to their machines and the WP 34S operating system has been modified to be able to use the IR to drive an HP 82240B IR printer One aspect of making the conversion is obtaining a serial interface cable to connect the HP calculator to a PC to down load the new operating system HP made a single batch of these cables and they are nearly exhausted HHC attendees of the last two Conferences have these cables and I hope that they will share them with others if they are not using them Eric Rechlin and others have these cables and they will offer a repurposed HP 30b to those who want the WP 34S machine but do not want to take the time to set up their own repurposing system Here is a list of HP Solve articles and commentary that will provide additional details HP 82240B IR Printer Issue 18 May 2010 Repurposing the HP 20b 30b Calculator Platform by Jake Scchwartz Issue 24 July 2011 page 22 From the Editor WP 34S memory up date etc Issue 25 October 2011 page 58 HHC 2011 Report
40. ed quite a number of new algorithms that speed up convergence These algorithms calculate two and even three interim root refinements in each iteration While these methods succeed in reducing the number of iterations they fail to consistently reduce the total number of function calls compared to the basic Ostrowski s method For example Grau and Diaz Barrero proposed the following equations for their algorithm Yn Xn f xa f Xn 3 H Xn Yn fn 2f ys 4 Zn Yn M Yn 5 Xnt1 Zn M f Zn 6 The algorithm starts with a Newton step using equation 3 to calculate yn as the first interim refinement for the root Equations 4 and 5 yield a second interim refinement Zn Equation 6 provides the iteration s final refinement for the root The above equations show that each iteration requires two additional function calls needed to calculate f y and f z I compared the total number of function calls for Ostrowski s method with the Grau and Diaz Barrero method for different test functions The result 1s a mixed one as neither method consistently performed better In the reference section you will find a reference to one of many books written by Ostrowski The second cited reference is a paper by Walter Gautschi about the life works and students of Ostrowski Gautschi himself is a mathematician and one of the last students of Ostrowski Gautschi has published books in the field of numerical analysis The third cite
41. egisters display a tagged or commented value Simply press the R S key to resume program execution ITER 4 Fig 8 The number of iterations 5 The program displays the improved guess for the root as shown in Figure 9 Again the figure shows the alpha and X registers displaying a tagged root value ROOT s cc icbb55e 1853 Fig 9 The refined root value You can press the R S key and resume at step 3 Enter the initial guess of 1 to locate the other root for the function The calculator displays the refined root of 0 025023481 in 4 iterations Remember that you can evaluate the currently coded function f x by entering a value for x and then pressing the key D I encourage you to edit the code in LBL D in Table 3 to replace the currently coded function with the ones that appear in Table 2 HP Solve 28 Page 16 Page 9 of 10 Observations and Conclusions The article introduced you to Ostrowski s root finding method This fourth order method excels over Newton s second order method and Halley s third order method While Ostrowski s method has inspired new algorithms that further reduce the number of iterations the basic Ostrowski method remains the most optimum as far as the total number of function calls In addition to introducing you to the Ostrowski method the article also presented two example listings the BASIC like program for the new HP 39gII and the RPN program for the repurposed HP 30b WP34S My hope is th
42. ensive finance calculator the HP 27 This was a special calculator because of its unusual mix of business and scientific functions The HP 27 has 10 data registers RO R9 with full register arithmetic A display indicator OF indicates when register values exceed 9 9999999 x 10 A clear storage register function clears all registers R4 R9 are shared with the finance functions R7 R9 and the statistical functions R4 R9 Even some of the stack registers are used altered The penultimate member of the Woodstock series 1975 1977 was the HP 25C The difference was the suffix letter C for Continuous Memory This meant that data registers and program memory retained their contents when the calculator was turned off HP Solve ft 28 Page 22 Page 4 of 10 i Automatic Primary indirect Continuous memory and even more data registers Memory Storage Storage The last machine of the Woodstock series is the HP 29C The HP Stack X Registers Registers 29C 19C has 98 program steps and 30 data registers designated as shown in T Ro Rao Fig 11 Z R B Y R Ris Sixteen of the 30 are primary storage register addressed as RO R 5 The X R Ris remaining 14 registers are indirect storage registers addressed by placing the LAST X R Riz register number RO R29 in RO and executing the STO I function These 2 Rew 30 registers may have their values indirectly stored recalled and operated on R Reza with storage
43. erstanding I remember hearing this maxim Yesterday I read a book and I leaned nothing today I read a book and I learned something HP Solve 28 Page 37 Page 1 of 3 In addition to knowing the multiplication tables students should also learn the reciprocals of the single digit numbers including the obvious 10 One of the important reasons for memorizing reciprocals is in expressing percentages Digi N 1 N Digi N 1 N Digi N I N 2 0 500 5 0 200 8 0 125 3 0 333 6 0 167 9 0 111 4 0 250 7 0 143 10 0 100 Mathematics is taught differently around the world Mathematics is taught differently today than it was taught when I was in grade school No matter how you leaned basic mathematics e g the grid method or chunking you have to know the basics mentioned above multiplication tables and reciprocals Approximating the Answer Example Part of the argument against the use of calculators in the classroom is that students will loose or never learn a practical sense of numerical calculations There was a time that students were taught how to extract a square root by hand Why is all this important I am reminded of the primary maxim of the reporter Never ask a question in an interview that you don t know the answer to Making numerical calculations should follow the same slightly modified maxim never use a calculator calculation that you don t know the approximate answer to I was reminded of an approximation technique I lea
44. extends over a dozen decades of values I was reminded of this when I had to unpack my electronics components and sort them into bin values Table 1 illustrates the value range of a very common component resistors This range of values is common place and actually extends several decades in both directions beyond the table in more specialized applications Table 1 Common Range of Electronics Resistance Values Decade Example Prefix EEX Comments lt 0 0000001 Super conductivity l0 on Materials studies Micro ohms uQ Hrs 0 001 Switch contacts Milli ohms mQ 10 0 01 Auto starter wiring 0 1 House wiring AA cell i Ohms Q 10 Low end of most Digital Multimeters DMMs 10 100 Watt bulb cold 100 100 Watt bulb hot 1 000 Kilo ohms kQ 10 10 000 Human body 100 000 1 000 000 ESD dissipative Mega ohms Q 10 10 000 000 High end of most Digital Multimeters DMMs 100 000 000 Hi Voltage dividers 1 000 000 000 Giga ohms GQ 10 gt 1 000 000 000 000 Insulator resistance Tera ohms TQ 10 Electronics 1s like any technical discipline in that certain units tend to be favored in practice In the mechanical field for example a length measurement of millimeters 1s often used Bolt or wrench sizes are in millimeters e g 18 mm vs 1 8 cm In the very early days of calculators that featured English Metric conversions it was inches centimeters Today it is usually inches millimeters to better match the units in most common use El
45. fix operators as a full blown parser does A full blown parser was implemented by others in much later HP machines 4 x The worldwide HP Calculator user Group known as PPC new models caused the name change was founded in June of 1974 The club publications long before the Internet provided programs and technical information to greatly increase the usage of HP s calculators The leadership of PPC continues today with HP calculator user activities such as small group meetings and the HHC Conferences 5 The HP 70A was an unusual business calculator for several reasons other than the data register usage The HP 80A replaced the double wide ENTER key with SAVE The HP 70A brought it back with a bright orange color The double wide ENTER key was then retained on business calculators going forward Collectors actively seek this machine because it is very difficult to find 6 x The HP 45A timer could be invoked by pressing RCL and then pressing CHS 7 6 all at the same time Once in timer mode CHS toggled it between timings and stopped HP Solve 28 Page 27 Page 9 of 10 Store and Recall on HP Calculators Notes Continued 7 The HP 67A was part of a matched pair of calculators The other machine was the HP 97A which was a thin desk top machine with thermo printer Programs without printer functions could run on either machine 8 The HP 29C was part of a matched pair of calculators The other machine w
46. ge 34 Page 5 of 6 The primary current measuring procedure is as it always has been Start at the highest current range and work your way down as needed The issue with measuring calculator current 1s that the current will change with the various operating modes and conditions the calculator is used The current drawn by the machine will range from sub microamperes to tens of milliamperes When you try to make a current measurement with your meter and it doesn t work you will soon learn that you violated this most important rule when making current measurements and you blew a fuse Don t feel bad EVERYONE has done it and EVERYONE will do it again That is why making current measurements is more difficult than other fundamental electrical measurements How much current does your HP calculator draw That is the subject of another article Measuring Calculator Current Notes 1 Drawing that first even very small test amount of current from a new battery will start the chemistry working and the battery will have its life determined from that moment forward 2 The hook shown is a lower cost knock off of the E Z Hook model XG31 See the technical details at http catalog e z hook com item test hooks Il categories test hooks e z micro hook lock hooks xg3 1 These cost about 4 each and they are a vital requirement for making measurements on calculators HP Solve 28 Page 35 Page 6 of 6 Is That calculator Answer Correct HP Sol
47. gister to start root building new text e GUE oo ixSY soo Bi 0i LBL 00 Start of the main loop In L STO 01 Initialize y x e RO j 2 If you are familiar with programming the HP 41C and to a lesser extent other RPN programmable calculators like the HP 11C HP 15C and HP 35s the above listing should be somewhat familiar to you You will still find in Table 1 a number of new and different programming commands and features that are special to the WP34S These new and different features are 1 The program supports alphanumeric labels that are up to three characters long The first command is LBL OST which complies with this feature This feature differs from the six character limit of alphanumeric labels in the HP 41C 2 The WP34S calculator has four user defined keys labeled A B C and D They help you to easily execute code that you place after LBL A LBL B LBL C and LBL D respectively The program in Table 1 uses the labels for keys A B and D By comparison the HP 41C has more than four user defined keys 3 The program uses LBL D to code the target mathematical function f x You can evaluate the function at any value of your choice by entering that value and pressing the key D The code for calculating f x uses the local variables feature The command LocR n dynamically allocates n local registers The command also makes available 16 local flags regardless of the value of n The WP3AS allo
48. had a substantial amount of memory and it had four I O ports The HP 41 is more than a calculator it 1s a calculator system Prior to the HP 41 calculator models changed frequently and a product life of about 18 months was normal The HP 1979 calculator lab manager Bernie Musch suggested that because the HP 41 was a system it would have a product life of at least five years He was happily mistaken when the HP 41 product life was double his expectations Because of the unique HP Corporate wide support given to the many accessories of the HP 41 it was used in every technical field from engineering to space exploration and by everyone from students to doctors The first basic model the HP 41C had 63 storage registers expandable with memory modules or an HP 41CV to 319 RO R318 registers These registers could be used for both program memory and data storage in a manner similar to what has been previously described except that the user specified the number of registers with a size function Memory reallocation was not an automatic process The memory organization is shown in Fig 18 The user executes SIZE and then provides a number in response to a prompt similar to the STO function Each data register uses seven bytes of program HP Solve 28 Page 25 Page 7 of 10 Automatic Primary Extended memory Memory management Memory Data Storage Data Storage JE Stack Registers is a bit involved because of the Rool many combina
49. he most recent HP calculator is shown at the shown on the poster on the upper left Type 1 shown bottom right Prod means it is current production The poster calculators are of two orientation types vertical format 85 and horizontal format 22 Horizontal format calculators are 20 6 of all HP calculators made Because the Palmtops were an outgrowth of HP s calculators it is natural to include them An example of the accessories and miscellaneous images is shown in Fig 4 The I O and OS legend is shown in Fig 5 Fig 2 illustrates the use of the Legend in the right bottom corner The information for each calculator model provided on the improved poster includes the following High resolution photograph keyboards are readable with a magnifying glass Code name of the calculator some are numbers Introduction date of the calculator Discontinuance date of the calculator The family name or grouping classification of each calculator The operating system logic system of each calculator The I O options of each calculator Version information of special calculators e g 25 30 or 35 anniversary versions Display representation in every image of every calculator Individual images of variations of special machines e g four types of the HP 35A Calculators of same model number are noted with connecting arrows HP Solve 28 Page 47 Page 4 of 7 TOPCAT CLASSIC HP 55 HP 35 HP 35 HP 35 5 Merlin n
50. holds four N cells connected in series to apply 6 volts DC to the calculator See Fig 1 Each calculator has its own specific mechanical requirements but the basics Fig 1 HP 41 N cell battery pack WT f EF Til y Y HP Solve 28 Page 31 Page 2 of 6 described here will apply to most calculator current measurement situations I favor inserting a piece of double sided circuit board between the battery contact and the calculator Newer machines will require a much thinner circuit board The space is often very tight especially with coin cells and I have even used folded aluminum foil covered with scotch tape Fig 2 shows the details of a piece of circuit board The soldered leads covered with heat shrink tubing are shown in Fig 3 This provides a physically strong assembly 1 4 inchs wide 1 1 8 inches long 0 04 inches thick Fig 2 Double sided printed circuit board PCB Fig 3 PCB with leads attached I have several HP 41 s with spare parts I modified one battery holder by filing a notch as shown in Fig 4 by using a square file The notch is on the negative end of the N cell holder I did this many years Sees ago and I don t remember why I chose this 2 end Fig 5 shows the battery pack installed with the current probe in place The current Fig 4 HP 41 Battery holder with filed notch at negative end probe may easily be pulled out Inserting the probe requires holding it
51. ible to key data into program memory Each digit sign decimal point and EEX required a program instruction Depending on the number of digits etc the 100 program instructions could consist of the data followed by a STON This data is then recorded on a magnetic card To store data in the nine data registers you read the card and press the R S key This process is much easier and faster than storing the data as needed An example would be English Metric conversion factors for a program Memory was very limited and the magnetic card off line storage was a powerful asset for a machine that lost all memory when the power switch was turned off Register use is re defined Choosing Addressable Registers Except for the case of registers Rs and Rg it is immaterial as to which registers you use Rs is the special object of the Decrement and Skip on Zero Bl DSZ operation presented in Section 4 which uses it as a de scending counter index in program applications If this use is contemplated R should be avoided for other uses Otherwise it may be freely used R is subject to alteration by the trigonometric functions includ ing the rectangular polar conversions and the relational tests used in programs These functions use R for intermediate cal culations scratch At other times R is available for your use The following operations destroy R siN trigonometric functions and their inverses relational test
52. ications in the field Cell phones and smartphones have calculator applications built in and most of the other personal electronic devices such as handhelds tablets and even laptops include the ability to load just about any calculator model of choice as an application Integrating calculator applications into other more popular electronics devices is frequently talked about using the term convergence Convergence is often used as an example of the death knell for calculators Yet year after year calculators continue to be sold by the tens of millions I personally believe that one of the major reasons calculators continue to be popular is that they are inexpensive easy to use and efficient They instantly turn on they have well designed keys and menus and they are very efficient Efficiency Efficiency is an objective term Itis not an opinion or a judgment It is defined as that ratio of input to output expressed as a percentage the higher 100 is highest the better While the application of this ratio 1s not usually applied in the testing or evaluation of calculators a comparative number of two machines or systems are frequently used The most common efficiency comparison is keystroke counting The argument is that solving a problem with three keystrokes is more efficient than solving it with five keystrokes How important is this Obviously it 1s but there are exceptions One argument is made that keystroki
53. ics 5 2011 93 109 About the Author Namir Shammas 1s a native of Baghdad Iraq He resides in Richmond Virginia USA Namir graduated with a degree in Chemical Engineering from the University of Baghdad He also received a master degree in Chemical Engineering from the University of Michigan Ann Arbor He worked for a few years in the field of water treatment before focusing for 17 years on writing programming books and articles Later he worked in corporate technical documentation He is a big fan of HP calculators and collects many vintage models His hobbies also include traveling music movies especially French cal movies chemistry cosmology Jungian psychology mythology statistics and math As a former PPC and CHHU member Namir enjoys attending the HHC conferences Email him at nshammas aol com HP Solve 28 Page 17 Page 10 of 10 Store and Recall on HP Calculators HP Solve 28 page 18 Return to top Store and Recall on HP Calculators The First Decade Introduction Most calculators even the lowest cost minimal featured ones have the ability to store and recall at least one number The first HP calculator the scientific HP 3 5AXO introduced in January 1972 had one storage register Two keys STO and RCL were dedicated to this feature See Fig 1 In nearly every case the memory storage register Fig 1 HP 35A has the same capacity as the display and it is dedicated to the user s use
54. iterative solutions of large linear systems Ostrowski passed away in 1986 in Montagnola Lugano Fig 1 Alexander Onan Switzerland He had lived there with his wife during his retirement The Algorithm Ostrowski tackled the problem of calculating a root for a single variable non linear function in a new way Most of the methods we know perform a single refinement for the guess of the root in each iteration Ostrowski s novel approach was to obtain an interim refinement for the root and then further enhance it by the end of each iteration The two step iterations in Ostrowski s method use the following two equations Yn Xn f Xn f Xn 1 HP Solve 28 Page 8 Page of 10 Xn 1 Yn f Yn Xn Yn f xa 2t ya 2 Equation 1 applies the basic Newton algorithm as the first step to calculate y which Ostrowski uses as an interim refinement for the root The iteration s additional refinement for the root comes by applying equation 2 Ostrowski s algorithm has a fourth order convergence compared to Newton s algorithm which has a second order convergence Thus Ostrowski s method converges to a root faster than Newton s method There is the extra cost of evaluating an additional function call to calculate f y in Ostrowski s method This extra cost is well worth it since in general the total number of function calls for Ostrowski s method is less than that for Newton s method Ostrowski s method has recently inspir
55. k s case it is assembling high resolution calculator images into a poster format Seven years ago Rick printed a 10 row poster of all of HP s calculators He has now updated that poster with a new 12 row one that is about as complete as you can get in having all vital information related to all HP calculators in one place The new information included in the revision is extensive Fig 1 and Fig 2 show the first HP calculator and the most recent calculator respectively Fig 3 shows a low resolution overview of the poster to give you some idea of what the 18 x 24 size contains The approach most enthusiasts use 1s to put as much information as possible in the space available Since the aspect ratios of HP machines varies it is not possible to arrange them in neat regular rows and columns The odd space must be used and many calculator related items are also included I made a poster image count and here is what I discovered in addition to the poster source two HP desktop tables and a legend Table 1 Poster Image Categories Calculators unique models 107 Palmtops 4 AccessorieS 8 MISC rop bo dee bow dees 8 Non calculator SM 400 970 2 HP Solve 28 Page 46 Page 3 of 7 HP 39qll Graphing Calculator 459 616909 i2 Dee ENTER TA CLASSIC n o HP 35 HP 39gII 7 N Ist Scientific q Aspen amp Fig 1 Four variations of the 1 HP calculator are Fig 2 T
56. llowing offices and cubicles Even today employees feel that they are part of a family When times are good the family shares the prosperity through profit sharing checks liberal fringe benefits etc When the economy is down Hewlett Packard does not lay off its employees who know the H P philosophy and will work a 4 day week if asked to In March 1968 Hewlett Packard introduced the HP 9100A table top programmable calculator At that time Bill Hewlett wondered if the next calculator developed could not be a tenth the size and cost of the 9100A Later the goal was formalized to be a series of ten machines to be hand held battery operated and capable of being carried in his shirt pocket which was measured on the spot Thus the HP 35 80 45 81 46 65 70 and 55 were born along with machines yet to be announced This brainstorming effort was being carried out in earnest by the newly formed Advanced Products Division by the fall of 1970 The technological accomplishment was in getting the HP 35 to market from concept to announcement in less than 18 months Operating by the Philosophy of providing technically advanced products of high quality based on excellent executive direction Hewlett Packard continues to be the leader in the electronics industry Traditionally H P has not sold its products to the general public The Advanced Products Division with its pocket calculator was the first market of this type that the company enter
57. me of the arguments made to discount calculator usage Read more HP home Support amp drivers HP respects your privacy If you d like to discontinue receiving e mails from HP regarding special offers and information please click here For more information regarding HP s privacy policy or to obtain contact information please visit our privacy statement or write to us at HP Privacy Mailbox 11445 Compaq Center Drive W Mailstop 040307 Houston TX 77070 ATTN HP Privacy Mailbox 2012 Hewlett Packard Development Company L P The information contained herein is subject to change without notice Graduate to HP Calculators HP Solve 28 page 2 Return to top ht with thigh sch Mator in lege Sroom Graduate to HP HP 10bil HP 10bll All Purpose Financial Calculator has every function you need to master business finance and accounting courses plus a robust set of statistics trigonometric HP 50g HP 50g High End Graphing Calculator was developed by engineers for engineers Tackle complex problems in advanced math and engineering courses with an extensive equation library multiple equation solver algebraic and math functions to carry you built in mathematical constants a range through general education math and science of unit conversions and 3D graphing requirements capabilities For more information visit www hp com calculators Copyright 2012 Hewlett Packard Development Company
58. memory register K will probably be most convenient to use in STO M You recall by repetitive calculations where one value remains the same constant efficiently pressing M Although the store and recall functions work identically for both memory registers since each has been assigned special purpose features to extend its use we have described them separately The M key provides a summing function The K register is similar Fig 5 HP 70A STO RCL keys Fig 6 HP 70A OH description of data registers except that K has a default value of 12 an obvious monthly number stored in it when the machine 1s turned on The M key idea 1s used on machines such as on the HP 01 HP 10A HP 10B and HP 21 Classical RPN data register addressing method is expanded further The Classic RPN issue of addressing registers e g R1 R9 is explained by Tom Osborne in Note 3 Statistical functions need registers conversion and scientific constants need registers Users found that entering numeric data from a program was relatively slow so computational variables stored in a data register offered several advantages These and many other justifications provided the need for additional numbers of data registers The programmable scientific HP 55A calculator was introduced a year after the HP 65A 1 7 75 The feature that made the HP 55A famous was its crystal controlled timer HP 45A users discovered that the code for the timer was included in the HP 45A
59. n I run across an article on the Internet that reminds me of the past With HP having grown so large and the founders that gave the company its name long gone I thought that I would reprint a few words I wrote over 37 years ago In memory of Bill and Dave From 65 Notes V2 NI P3 January 1975 In January 1939 two Stanford Electrical Engineering graduates flipped a coin to see if their partnership would be called Packard Hewlett or Hewlett Packard David Packard lost on that flip and Bill Hewlett had his name first The occasion was the receipt of the first big order from Walt Disney Studios for nine audio oscillators called the Model 200A The early experimental workshop was literally a garage oper ation In 1947 the firm incorporated and annual sales reached 1 5 million New products were added to the expanding product line of signal generators microwave instruments amplifiers etc and by the 50 s the company was developing instruments at the rate of 20 new ones per year HP Solve 28 Page 49 Page 6 of 7 The strong leadership exerted by Bill Hewlett and David Packard is what has made Hewlett Packard the unique company it is today Another key factor has been people the employees Over 20 000 people work for Bill and Dave who hold 5196 of the company stock The company operates on policies that strongly reflect the philosophy of the two men The open and free exchange of information among engineers and designers 1s encouraged by not a
60. n of the answer as a check for the answer obtained by the calculator This article provides a few techniques for approximating the answer to making numeric calculations Calculations involving exponentials or trigonometry calculations are special cases and beyond the intent of this article They would however be of greater interest to the specialized practitioner Is That calculator Answer Correct Notes 1 For a discussion of other non calculator methods that were used before calculators see Calculating Before Calculators in HP Solve Issue 21 page 27 http h2033 1 www2 hp com hpsub downloads Newsletters HP Calculator eNL 12 Dec 2010 vl pdf 2 The topic of learning math will be a topic of debate forever In a modern complex high tech world we all have to be able to differentiate between a wide variety of measurements In the engineering world there is a saying that if you can t measure it you can t control it Measuring requires numbers and numbers requires mathematics 3 The name The rule of nines is used for many purposes including medicine assessing body burn area and accounting fraud as well as being the name of a band In nursing the rule of nines refers to body surface area HP Solve ft 28 Page 39 Page 3 of 3 Calculators and Prefix Units HP Solve 28 page 40 Return to top Calculators and Prefix Units Richard I Melson Electronics is probably one of the most diverse fields where the range of units
61. ng time is irrelevant in that even for the highest paid calculator user the keystroke saving time is so small as to be deep in the user time usage noise Time wasted on other non work related human activity telling jokes drinking coffee etc 1s far more wasteful and inefficient This perspective poses that even thinking about the time saved by more efficient keystroke sequences is just plain silly Another perspective related to efficient calculator usage 1s speed or the time spent on solving a problem It s all about being human Calculator speed is like driving a car Some most prefer to drive fast Why is this I am sure that there are many studies to explain the obvious that include such factors as male female emotional state being late owning a fast car etc I will offer what I consider is an important consideration boredom When human beings are seriously working on a problem they tend to focus on getting it done The computational part of the problem is done by the machine so in the mind of the problem solver calculator speed is a process step that is out of the calculator user s control If the problem involves many calculations or repetitive calculations the calculator user gets a bit frustrated 1f everything doesn t go smoothly and quickly I was using a non HP calculator clone because that was all that was available at the time and place I was problem solving I was exploring a number of electronics ci
62. onds These two numbers are the arguments for the BEEP command which produces the sound The number following the BEEP 1s the argument for the WAIT command which will wait for the duration in seconds A second BEEP Wait sequence follows for the second tone In the case of ALMT a higher tone follows the lower tone which is the reverse order of tones of ALM2 The end of the DO clause is the UNTIL command which is followed by the KEY command The Key command will cause the loop to be terminated when a key is pressed The END is then executed and the DO Loop is terminated The last command DROP is used to remove the unused key code that the KEY command places on the stack HP User Community News HHC 2012 The final arrangements for HHC 2012 were not quite finalized as this issue was being prepared to be mailed and posted A venue change was made at the last minute It is good that the HHC Committee had a Plan B The Conference this year will be held in Nashville TN on September 22 amp 23 The hotel and travel details will be posted hopefully by the time you read this at hhuc us The Calculators of HP Poster Rick Furr is an HP calculator fan Like most fans he has a website vcalc net A few HP fans get so enthusiastic about their hobby that they apply their knowledge and experience towards a calculator related project In the 38 years that I have been writing about HP calculators I have reported on hundreds of such projects In Ric
63. oom and at what year I remember attending a math conference session on this topic in a Los Angeles school The presenter was making the argument for allowing calculators in the classroom when he just stopped talking After a moment he asked What time is it Like zombies everyone in the room looked at their wrists He pointed out that we all have a natural sense of time but since we have a mechanical device to provide an accurate time we use it Why shouldn t we use a mechanical electronic device to make accurate calculations Looking back the pro calculator teachers won While calculators are able to take the drudgery out of mathematical calculations we still have to under stand what the calculations mean We still must understand the idea of division and multiplication We MUST learn our multiplication tables 12 x 12 or as they used to do in the UK 13 x 13 We must learn i e Memorize certain mathematical relationships Can you quickly answer the following questions from memory 1 What is 7 x 8 2 What is 12 x 12 3 What is 1 5 expressed as a decimal 4 Which is larger 1 5 or 1 8 and by how much The reason for learning and memorizing certain mathematical relationships is very simple Human beings learn best by going from the specific to the general The specific 1s our reference point We just know it and we then compare the unknown to our known a standard 1f you wish and we are better able to grow in our learning and und
64. oot value koot 223 200921962 I encourage you to edit function MYFX in Table 1 and replace the currently coded function with a different one Table 2 shows a list of additional test functions The table also includes columns that show the recommended initial root and the final root you get Using the tolerance value of E 8 should be adequate for the test functions in Table 2 Table 2 A List of Additional Test Functions Mathematical Function Initial Guess for the Root Root f x x 4x 15 1 6319808055661 f x x exp x sin x 3cos x 5 1 2076478271309 f x sin x x 2 1 8954942670340 f x 10 x exp x 1 f x cos x x f x sin x x 1 f x expCx cos x The WP3A4S Listing Let me present the listing in Table 3 for my implementation of the Ostrowski method on a WP34S calculator The program labels appear in red characters so they are easier to locate The emulator I used for this article 1s running version 3 of the calculator software HP Solve ft 28 Page 12 Page 5 of 10 Table 3 The WP34S Listing Program TAG Comment es Step um Dudum m Re nena evaluate the lone EEX Rc 00 Eo o iati Store fix STO 05 Store 1E 8 in register R05 as the RCL 00 initial tolerance value RO LBL D Labelusedtocodef x 0 Jt Za O R 01 and R 02 mm Ea RR UM MEME MEME NNMN
65. ove comprise the calculators that HP made in the first five years of calculator manufacturing These are the machines of the historical Classic series Fig 10 Top HP 21 STO and RCL keys Following the Classic series is the Woodstock series of HP calculators These were smaller and lighter and they picked up where the classic series left off There are four scientific models and two business models The Woodstock series is a transition series in that Continuous Memory first appeared towards the end of the series The low priced HP 21 was the entry Scientific model having an M data register The next scientific model was the HP 25 and it was programmable with 49 steps It has eight data registers RO R7 storage register arithmetic and register sharing with the statistical registers R3 R7 The HP 25A was famous because it was cost effective and the HP user community considered it a great challenge to squeeze many advanced level programs into its limited memory Keying 49 steps for a program wasn t a tremendous time challenge and was reasonable because turning the calculator off cleared all memory Right Shifted Memory function keys provide register arithmetic Along with the HP 25A came the third finance calculator the HP 22 with its ten data registers RO R9 Register arithmetic was also provided and R5 R9 were shared with the statistical functions The next calculator was a more capable and more exp
66. p so a ist Scientific type 2 type 3 1st Business s 3 73 5 73 1 70 1 75 1777 m HP 67 3 Wizard Superstar m Hawkeye wees eget Hon mm imorlagy dam ti Pe ia Liam mesa x 3 o HP 970A o Handheld DVM Be v e Gold classic Charger o Cricket z HP 01 HP 21 m HP 25 R HP 27 Silver A Pumpkin 5 Turnip Squash amp Salad s 3 4 41 65 67 97 WwW x Dm a Ww ul o rn TS ezo 922676 Merlin HP 75D Wand EUNT Y 71175 Moa Card 1l 107 521064 3 Module gt 2 821704 jam iss 50 e OI T e E Extended Funet Clide e lt q u z M AIDIA um 485X Demo pr vin b n M ard mar 82104A Card Rdr i TOT emory ul c Hyster s E uj C 93 II N eem eala EE 1A a e g B2143A 4 9 79 L8 2 3 Peripheral Prister o HP 41C 2 MP 41CV 8 gHP 41 c ev g 2 HP 41CX 3 82342A 11 87 313 Bo Coconut 4 Silverbird gt z 9 Honeynut 5 49 Cards ER Module d I 1 1 imo Blanknut Blinky L 5 IMMO heer mm 3 HP 485X E 582160 HP 1L Grapenuts ES g g Charlie act rown 12 77 HP 975 Ricochet 19852 PALMTOP 3 95 95LX Demo Memory Card VOYAGER B R CHARLEMAGNE HP 95LX Jaguar Thermal Printer Special K 521534 1932 B 9 Video Interface g HP 15C gs HP 16C 22 HP 12c Platinum z n HP 48GX 2 2 HP 48G 3 HP 48G 2 HP 49G H
67. proach allows you to store the root for additional inspection You can invoke functions MYFX OST and GO from the command input line After you key in the three functions in Table 1 you can run the program by performing the following tasks l Type GO at the command input line The function GO first displays the Tolerance input form shown in Figure 2 You can enter a new value for the tolerance and then press the OK menu option which is associated with the F6 menu key or simply accept the current tolerance value and press the OK menu option Tolerance BEEN Tolerance ONERE NEN Enter tolerance for the root y o o eej eae Fig 2 The prompt for the tolerance value 2 The function displays the Initial Guess input form shown in Figure 3 If the current guess is not 50 type in 50 and then press the OK menu option Otherwise just press the OK menu option Initial Guess ooo Enter initial guess for the root EIT Fig 3 The prompt for the initial guess for the root HP Solve 28 Page 11 Page 4 of 10 3 The function displays the number of iterations using the message box shown in Figure 4 Click the OK menu option to resume program execution Number of iterations 4 GO pK Fig 4 The number of iterations 4 The function displays the value for the root using the message box shown in Figure 5 Press the OK menu option to end the program GO C a a ee S Fig 5 The refined r
68. r with more than 10 numeric OS ee NIME du0 memory cells then RPN would have won because it saves Press See displayed a keystroke STO 11 would have to be STO 11 Enter eb 1 EX X display vs 11 STO The HP 45A was the first to add the zx feature of register arithmetic Fig 2 shows how the HP Fig 2 The HP 45 Owner s Handbook explains 45 Owner s Handbook explains register arithmetic register arithmetic on page 27 HP Solve 28 Page 19 Page 1 of 10 Tom s brilliant engineering set the tone very early for keystroke efficiency a hallmark of HP calculators Register arithmetic makes perfect sense when memory is scarce expensive A data register 1s then able to serve multiple purposes The most obvious example of multiple date register use is as a summing register The HP 45A is not programmable but using register arith metic in a program could increase program efficiency as well The nine storage registers of the HP 45A R1 R9 Restricted Storage Registers R R Registers Rs Rs are used internally when performing summations using z and Su z s When summations are not being performed these registers may be used for general purpose storagc However since registers Rs R are not overwritten by new values they must be cleared of existing values by pressing i cien before they are used in summations Register R Register R is required internally when performing trigonometri
69. rammable HP calculators In this article I present the Ostrowski root seeking method which I consider a gem of an algorithm that has not received much publicity until somewhat recently I also present listings for Ostrowski s method to run on the WP34S calculator using a repurposed HP 30b and on the new HP 39gII Before I discuss the algorithm and present the two listings I would like to first shed some light on the person of Ostrowski Ostrowski A Short Biography Alexander Markowich Ostrowski 1893 to 1986 was a talented Russian mathematician who was gifted with a phenomenal memory He was studying math at Marburg University in Germany when World War I broke out He was therefore interned as a hostile foreigner During this period he was able to obtain limited access to the university library After the war he resumed his studies at the more prestigious University of Gottingen and was awarded a doctorate in mathematics in 1920 He graduated summa cum laude and worked in different universities He eventually moved to Switzerland to teach at the University of Basel before the outbreak of World War II Ostrowski fared well living in that neutral country during the war He taught in Basel until he retired in 1958 He remained very active in math until late in his life This gifted and prolific mathematician was engaged in various mathematical problems The advent of computers catapulted Ostrowski to delve into numerical analysis He studied
70. rcuit configurations and the calculator had a terrible keyboard I was forced to press each key and visually check the display to see if the key responded Since I wanted the full ten digit accuracy I was pressing a large number of keys for HP Solve ft 28 Page 52 Page 1 of 3 just a few dozen calculations The calculator was clearly getting in the way of problem solving Is keystroke counting important Yes itis Is the calculator response time important Yes it is A program is always faster The machine I had to use was an RPN keystroke programmable and I entered a program to save time while making notations on a napkin In terms of HP 15C Programming typical RPN operations and structure I thought of how the program should be approached The program starts assuming that the two variables A amp B are used for R1 amp R20 are on the stack as shown in the START column My first program sketched on a napkin was the most general straight forward method of storing the variables in a register and recalling them as needed In this example each variable is needed twice See Fig 1 below This is the easiest to program and stack usage is simplest with only a concern that the stack is not overloaded This approach required nine program steps Step 2 3 4 5 6 7 8 9 10 T pU TS T iu T es n T ae E E a a ao AXE B E Y A A B B AXB A AB B X B B A A AxB A B A B AxB A B AxB A B press START STO2 xey STO x RCLI RCI2 R S
71. rent may range from femtoamperes to kiloamperes 18 decades The RPL graphing calculators have a great unit management system It would be even better however if the common units could be presented as an input output menu with the prefix values that are used in practice If I were making an ohms law calculation I would like to be able to input voltage in millivolts or volts or kilovolts etc resistance in megohms or ohms kilohms etc and get my answer in microamperes or milliamperes etc This would make problem solving even more convenient An example where this would be especially useful is a problem wherein the prefix units are provided and I am not familiar with them I could just input the values as I find them How could this concept be implemented Perhaps there could be a function called Prefix which would provide the options that would match the units in use The program would convert the sub or multiple units to the basic unit do the calculation and then convert the basic unit to the unit desired using a Prefix units menu A smart program would provide a labeled default prefix with a menu option to show it in other prefix units This prefix I O would be applicable to any type of problem and could be a part of the calculator software What do you think of this 1dea What kind of technical problems do you solve Do you use prefix units How do you imagine this could be implemented in practice Contact me at the email
72. rned while eating lunch and thinking about an electronics problem I needed to solve the equation that calculated the capacitive reactance of a capacitor using it as a 60 Hz voltage divider Xe l 2nfC I had a 0 01 uF capacitor What would be its reactance at 60 Hz One uF is a millionth of a Farad I then remembered that I really didn t need my trusty HP 15C HP 48GX or HP 35s Expressing the value of C in scientific notation is Ix10 Let s use a notation of 1E 8 The denominator 2zf is 2 x 3 14 x 60 or 6 2 x 60 or about 360 times the capacitance 360 x E 8 This is 3 6E 6 The reciprocal of 4 1s 0 25 so the approximate answer is 0 25E6 or 25E4 or in normal electronics values 250 K ohms When I make the calculator calculation and get 265 258 23849 ohms I am confident that all those digits are correct Reviewing Exponents 1 Approximate notation examples 1 000 1000E0 100EI 10E2 1E3 Notice how making the value before the E smaller by ten the value following the E gets larger by 10 Here is how small numbers work 0 0001 0 0001 E0 0 001E 1 0 01 E 2 0 1E 3 1E 4 The idea is to reduce any number to a single digit with perhaps a single decimal digit 2012 2E3 Rounding is necessary m 3E0 265 258 23849 2 7E5 or 3E5 2 Multiplying two numbers expressed in scientific notation with exponents adds the exponents Multiply 263 x 343 3E2 x 3E2 9E4 90 000 The calculator gives 90 209 3 Dividing two numbers expressed in
73. rs Notes 1 The classic model numbers 35 45 65 55 67 80 amp 70 are suffixed with A to avoid confusion with later models and to serve as a reminder of their history The HP 35A designation was used internally by HP and is documented in http hhuc us 2007 Remembering 20The 20HP35A pdf 2 The HP 80A Owner s Handbook is a shirt pocket size similar to the HP 35A but much thicker It did not have an Index but the detailed Contents provide a workable substitute 3 RPN Tip 14 may be downloaded at http www hp com large calculator augustO9 the rpn stack future past pt 2 pdf This is part 2 of an article discussing the Classical RPN stack Most readers may not realize that the HP 35A predecessor the HP 9100A was actually a combination of infix and postfix The electronics dictated the decision to go forward with Classical RPN in the machines that followed Tom Osborne further explains No one that I knew at HP Labs was familiar with RPN when I designed the 9100A The green machine I took to HP was an interesting combination of infix for multiply and divide but post fix for add and subtract The 9100A stack was high enough to solve most of the normal computations we encountered With a bit of mental parsing on the input a 2 deep stack can solve any two operand problem so we were more than covered A really deep stack 1s required 1f one goes formal and leaves all of the operands in their original order and then relocates the post
74. s Calculating in Addressable Registers Thus far all calculations have involved the X register or the X and Y registers to produce a result in X In the case of addressable register arithmetic the result is left in the addressable register and X is unchanged Subtraction To subtract x from r press sto n Addition To add x to ra press sTO n Multiplication To multiply x and r press sto X n Division To divide x into ra press STO n For example store 6 in register R and then increment it by 2 Press See Displayed Comment 6 STO 1 Stores 6 in R 2 sto 1 Adds 2 to r RCL 1 EZ Confirms that r equals 8 Now subtract 5 from the contents of R 5 sto 1 RCL 7 Confirms that r has been reduced to 3 Finally multiply the remaining contents of R by 2 2 sto x 3 ACU 1 Confirms that r has been increased to 6 Fig 4 HP 65 OM register arithmetic The next second finance machine the HP 70A9 introduced 8 1 74 had two data registers called the M HP Solve 28 Page 20 Page 2 of 10 and K registers Fig 5 shows how the keys were labeled and Fig 6 shows how they were described The M register 1s the Storing and Recailing Numbers familiar data reeister Two general purpose memory registers are provided apart from the g stack One memory register M is primarily useful when you need to Y ou store by pressing N store data for use in subsequent problems or for accumulation The other
75. s easy with the probe shown in Fig 3 You just solder a one ohm resistor across the probe and you may EA EAT change the meter range switch as much as you wish oer The low cost CEN TECH DMM however only has a 200 EE E i aly i s lis is i mV range as its lowest range and you will lose resolution 2 2 O D B M OH The one ohm is convenient because what you see in the display voltage wise may be converted to amperes 1 mV is mA Even meters 10 or 20 times more expensive do not offer sub DC mV ranges You may increase the resistor Fig 5 Current probe shown in place value to 10 ohms to add one more digit of resolution but you are then back into the region where certain calculators may not turn on or operate correctly under all conditions Certainly measuring microamperes is out of the question because a microvolt meter is much more expensive There is another consideration If you are measuring sub millivolts you will have lead length stray induced noise issues and your electronics understanding will be further challenged What is a user to do The technical issues are not too difficult and cost is not the issue As I mentioned above measuring current is a challenge but it does not have to be difficult Once again there is a mechanical solution that requires a bit of work What you need to add to your probe set up is a normally closed push button switch connected across the two meter leads When you want to measure the curren
76. st be slowed down or time conditioned in order to avoid confusing the digital circuits Calculators have special turn on circuits reset circuits that address the mechanical switch bounce of keys switches and users messing with electrical connections in trying to measure calculator current AII users have observed strange behavior when using their calculators and they intuitively know that this is the nature of digital circuits Computers are the same way and when in doubt restart reboot first Breaking the Circuit The mechanics of breaking the battery circuit of a calculator means that you must get your two meter leads between the battery and the power input of the calculator This is a mechanical problem and you just want to make a quick measurement I am sorry but making that quick calculator current measurement is not going to be very quick or all too often not very easy There is a resurgence in interest in the HP 41 because of Monte s Newt project the HP 41CL so I will use the HP 41 as an example of applying the concepts discussed above The first task 1s getting a DMM that has a low enough current range to measure at least as low as 1 uA fire Battery may explode oret CAUTION Do not connech m di properly charge or dispose of up to 10 mA as a minimum range s ma C m g C 3 E m P 5 BEEP De anoo fO awah pad aud P nay D Le Weel The HP 41 uses a spring loaded battery pack that
77. t could converge the calculator into them is that calculators are so efficient This article reviews what this means and dispels some of the arguments often made to discount calculator usage That is it for this issue I hope you enjoy it If not tell me Also tell me what you liked and what you would like to read about XY Richard Email me at hpsolve hp com HP 48 One Minute Marvels No 15 Two alarms One Minute Marvels OMMs are short efficient unusual and fun HP 48 programs that may be entered into your machine in a minute or less These programs were developed on the HP 48 but they will usually run on the HP 49 and HP 50 as well Note the HP48 byte count is for the program only Two Alarms Here are two simple repeating alarm sounds programmed to start when you press the menu key and stop when you press any other key ALM1 and ALM produce alternate low then high tones ALM2 is about twice as fast as ALMI AMT repeats about once per second HP Solve 28 Page 45 Page 2 of 7 ALMI lt lt DO 900 2 BEEP 2 WAIT 1200 2 BEEP 4 WAIT UNTIL KEY END DROP gt gt 15 commands 95 5 Bytes C3Afh ALM2 lt lt DO 1000 1 BEEP 1 WAIT 500 1 BEEP 2 WAIT UNTIL KEY END DROP gt gt 15 commands 95 5 Bytes FD5h Both programs are structured the same using a DO Loop to repeat until a test is made The number following the DO 1s the frequency in hertz The second number is the duration in sec
78. t you must cut or un solder the circuit and this is usually not convenient Current Range An interesting aspect of electronics 1s the very wide range of values that are involved Current is measured in amperes Your car starter may require 200 to 500 amperes to turn over the engine A digital watch may require a millionth of an ampere to run 1 1 000 of an ampere is a milliampere mA and 1 1 000 000 of an ampere is a microampere uA Nanoamperes and picoamperes are becoming more common specifications of IC currents in todays advanced low power IC s The current that a calculator will draw will vary greatly from low microamperes to low milliamperes This range of 1 000 to 1 may instantly change with the press of a key These highly variable electrical conditions add to the challenge of calculator current measurements These considerations are a Inserting the meter into the circuit a mechanical and technique issue b Using the correct meter and or range an experience issue c Keeping meter resistance under control an expertise understanding issue d Measuring and range changing an experience expertise understanding issue All of these issues apply and the last one needs further explanation When you turn on the switch of an electrical device current flows from the power source Suppose there 1s something very wrong and the device 1s shorted or presents near zero ohms to the power supply What prevents 1 000 amperes from
79. t you push the switch Now you may futz with your meter and calculator as much as you wish without concern of switching transients disturbing the calculator and you just press the button to make your measurement The calculator will always turn on when you need it to and you may change ranges as needed button is not pressed HP Solve 28 Page 33 Page 4 of 6 A More Modern Example Many current HP calculators use coin cells for the power supply Fig 6 shows an example Machines like the HP 20b HP 30b HP 10bII and HP 15C LE use the CR 2032 coin cell Fig 6 and fig 7 shows how the power connections are made There is no physical space to use a current probe approach described with the HP 41 example For this situation the cells are removed and power is supplied using clip leads and miniature spring loaded connectors that are small enough to grab on and hold the small terminals of the cell holder An external power supply of external coin cell holder is used for the power The current meter DMM is connected with the power source vn Qm Yos SS e ate oes s a delet 2a2 SITES AU i a tr E SEES CR 2032 Coin Cell Holder Fig 6 Coin cell holder with electrical connections buried Fig 7 Small cell metal connections ao s Yu 3 ry gt A L i SS Fig 8 Miniature clips attached to the cell terminals red positive black negative Fig 9 Hook close up HP Solve 28 Pa
80. tions of models nO HP 41CV or and memory modules for the four lis up aic HP 41C with expansion I O ports The HP 4 Memor TE If all memory modules Madulae a 41CX model provided additional H 5 e wore a iocatedto stor The Quad modules built in with maximum age registers each 63 Memory l additional module Rea Module memory would accountforthe l following register m Data registers could be recorded 99 l 318 m on magnetic cards the same Standard Ro amp and or ones as the HP 65A and HP 67A Module Rea oo Ri 100 126 Module 3 Rii91 254 Quad Memory Module Aside from the many ard party Module 2 R127 190 Module 4 Ri ss 31g Re3 es Ri00 318 memory products there were Fio 18 HP A1 M cation Th b dat other considerations for memory LQ emory organization user Sets the number of ala data registers e g the ALPHA St th the SIZE tion l A ud eee register could also be used to store data if necessary Another example is functions for the storing and recalling numbers into the stack registers Another example is the use of synthetic programming to access registers not normally available The HP 41 was a single line alphanumeric calculator and data storage requirements were impacted because a given register could store either a number or a small number 6 of alphanumeric characters All registers stack LAST X and Data could be used for alpha characters The basic
81. tor solvable Here 1s a historical review of how HP has managed the memory usage of the calculators of the first decade The decisions made in the 70 s still impact the calculators of today S05 Measuring Calculator Current You press the ON key and nothing happens now what You replace the batteries and you still have a blank display Do you toss the machine and buy a new one The most powerful technique to knowing what is or is not going on in the calculator is to monitor the current it draws by measuring the calculator current The meter is not expensive as low as 3 so why not check it out S06 Is that calculator Answer Correct How do you know that the answer you have just calculated is correct A few easy to learn or review techniques may be applied to approximate the answer so that you could even get by without the machine if you had to You need to know that all those numbers in the display are correct S07 Calculators and Prefix Units Calculators must be easy to use Here is an idea for making them even easier and more convenient for problem solving What do you think of this idea S08 Regular Columns From the editor One Minute Marvels HP User Community News HC 2012 The Calculators of Hewlett Packard Poster A Bit of HP History PH or HP S09 Calculator Usage Is Efficiency Important One of the reasons calculators are still so popular considering the many other devices we use every day tha
82. umerical table and plot views of any mathematical expression Educators have found that using these technologies allows students to more easily understand the connections between these representations and their underlying mathematical objects The expression shu xing jie he combine number with graph has been widely accepted as the golden principle for mathematics teaching since the 1960 s and demonstrates that Chinese Educators share similar ideas about mathematical representation A more recent project conducted by the Abant Izzet Baysal University Integration of Handheld Technology with the New Mathematics Curriculum provides an opportunity to explore how Chinese Educators and students use graphing calculators and the impact this has on how mathematics is taught and learned Page of 2 The HP China MOE Project introduced an approach now known as 3Y s from the Mandarin words for each concept that begin with the sound of Y The 3Y s stands for Useit Implement an effective teaching strategy that motivates students to use the graphing calculator and develop a high level of proficiency Useitfrequently Apply multi varied mathematical examples with the graphing calculator in every lesson to achieve greater learning results Use it properly Use graphing calculators to investigate and represent mathematical concepts to create enhanced learning ecosystems The HP China MOE Project along with the 3Y s mo
83. ve 28 page 36 Return to top Is That calculator Answer Correct Richard I Meloon Introduction Before calculators were the accepted means for making numerical computations the primary tool of choice for students was the slide rule While the slide rule was capable of getting a correct answer it had a major flaw The user had to keep track of the decimal point Essentially this required that the problem solver needed to solve the problem twice First you used a technique of approximation that would essentially provide the decimal point order of magnitude followed by the numbers of the answer provided by the slide rule If you talk to any teacher regarding the answers that students turn in for homework assignments or exams you will hear many stores about the wild answers that students turn in They think that they have the right solution and with all those wonderful digits the calculator provides it must mean that the answer is correct An experienced person such as the teacher will have a practical sense of the correct answer The student however doesn t have the benefit of an additional ten or more years of experience involving the application of the problem Does the average ant weigh 0 11 oz Oh that really was 0 00011 oz or 110 micro ounces 0 003 milligrams Learning Math Computational Basics In the early days of calculators there was a big discussion on weather calculators should be allowed in the classr
84. were unchanged and were the Continuous Memory versions with the same model numbers and a C suffix The models were Scientific HP 31E HP 32E HP 33E HP 33C HP 34C Business HP 37E HP 38E HP 38C The E Suffix meaning was hinted at in the HP newsletter HP Key Notes as Extensive low end product line Many users believe the E stands for Economy Fig 14 on the next page illustrates that the HP 31E was directed at students 60 in 1978 is equal to 213 73 today 9 The HP 31E Owner s Handbook was in two parts The basic 17 page booklet and a 56 page Solving Problems with Your Hewlett Packard Calculator Data register usage is described in the later booklet which was also used with several E series machines The HP 31E had four unshared data registers RO R3 Fig 13 shows the related data register keys Note the CLEAR REG function The HP 32E was the next E machine and it was a step up from the HP 31E The 32 was also nonpro grammable but added more conversions statistics and 15 data registers RO R8 and R 0 R 5 These registers also provided storage arithmetinc HP Solve 28 Page 23 Page 5 of 10 R 0 R 5 and the Y register were shared by the statistical registers The last E series scientific was the HP 33E It has eight data registers RO R7 with R2 R7 shared with the statistical functions Fig 15 shows the HP 33E data register designations Fig 13 HP 31E STO and
85. ws you to directly access the first 16 local registers using the dot as a prefix followed by two digits Thus to store a value in the first local register you use STO 00 Likewise to recall a value from the second local register you use RCL 01 Beyond the 16 register you must use indirect addressing The above code uses the command LocR 3 to HP Solve 28 Page 14 Page 7 of 10 dynamically allocate three local memory registers R 00 R 01 and R 02 The command PopLR de allocates the local registers It is optional and I am including it for the sake of demonstration By default the local variables and flags in a subroutine are automatically removed when the subroutine reaches a RTN or END statement 4 The program uses the alpha register to prompt the user for input and to display tagged commented output values By default the WP34S simply appends characters to the alpha register This feature is the reverse of HP41C s support for the alpha register where inserted text automatically overwrites existing text in that register Appending text in the HP 41C requires that you start with the special append character Thus to start inserting new text in the alpha register of the WP43S you must first use the command CLa to explicitly clear the alpha register Each program step can take up to three characters So for example to build the prompt text TOLER I need two program steps The first step inserts the first three characters TOL while the se

Issue 28 (July 2012)

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