Aurora AX-501
Contents
1. Example Key to Press Display ION C 0 5 5 x 5 ION C 0 6 6 x 6 8 8 CEJ 0 2 2 12 1 3 4 134 gt 13 3 133 3 Priority Levels in Calculation Operations are executed according to the following hierarchy 1 Function calculations such as sin and 2 Calculations in parenthesis 3 Powers and roots 4 x 5 Example 8 2x2 Key to Press Display ION C 0 8 8 8 2 2 x 2 2 2 12 X In the example above notice that the multiplication is performed first Performing 2x2 8 should give the same result as the preceding one 4 Parenthesis a Using Parenthesis The parenthesis allow changes to be made to the priorities of the operators For example to calculate 3x 8 5 If you leave out the parenthesis the multiplication between 3 and 8 is performed first then the subtraction of the result with 5 is made The presence of the parenthesis allows the subtraction of 8 and 5 to be made first and the multiplication of this result with 3 Key to Press Display ON C 0 3 3 x 3 0 8 8 J 8 5 5 3 9 In the above example the calculator waits2. is filed in the 1 8 sign register 8 is file in the register x and 5 5 5 replace 8 in the register y The calculation is 3 complete The key tallows an exchange between the content of the register x and content of the register y Take again the preceding example Key to Press Display Explain ION C 0 8 8 8 5 5 2ndF 5 The content of register x is display and 8 content of register y 5 goes into register x 3 Example 344 Key to Press Display 3 3 Ly 3 l4 4 2ndF 4 E 3 64 15 Factorial The calculation of n is made possible through the second function of the CE To calculate 3 for example press 3 first followed by 2ndF n 16 Random Numbers A pseudo random number with three significant digits can be generated by pressing 2ndF RANDOM Random number generation is not possible when binary octal hexadecimal system mode is set 17 Memory Calculations The calculator contains a memory that the user can use at any time Three keys are allocated for the management of this memory key STO puts the display number into the memor
3. Key to Press Display ON C 0 6 6 0 60 cos 0 5 X Attention before making any calculations check the angle unit display by the calculator 10 Logarithmic and Exponential Functions The natural logarithm and common logarithm functions are accessed respectively with the keys and log The second function of the key In is the inverse unction of the natural logarithm or natural antilogarithm 5 The second function of the key log is the inverse function of the common logarithm or common antilogarithm 10 11 The functions Square Root Power and Reciprocal The calculation square x square root x cubic root second function of the key x marked by3 x and reciprocal second function of the key x7 smarked by 1 x is the same as the one explained above for trigonometric functions The value x must be enter first before the chosen function For the universal power key ly and root second function of the key y markegby enter p ae the value for y first then the value for x x lt 12 Hyperbolic Inverse Hyperbolic Functions Example cosh5 7 sinh 9 4 tanh8 7 Key to
4. Make sure that the display appears as shown below If the display does not appear as shown reinstall the batteries and check the display once again 7 l f4 Fig 1 Fig 2 Automatic Power Off Function This calculator will turn itself off to save battery power if no key is pressed for approximately 7 minutes C Technical Specifications Calculation Ranges Within the ranges specified this calculator is accurate to 1 of the least significant digit of the mantissa However a calculation error increases in continuous calculations due to the accumulation of each calculation error This is the same for y V n e In etc where continuous calculations are performed internally Additionally a calculation error will accumulate and become larger in the vicinity of inflection points and singular points of functions Calculation ranges 10 9 999999999x 10 and 0 If the absolute value of an entry or a final or intermediate result of a calculation is less than 10 the value is considered to be 0 in calculations and in the display Range of Entry Function Dynamic DEG x lt 4 499999999 x 10 tan x x 90 2n 1 RAD x lt 785398163 3 sin x tan x Ix 5 2n tan x 1 GRAD x lt 4 999999999 x 10 tan x x 100 2n 1 DEG x lt 4 500000008 x 10 RAD x lt 785398164 9 GRAD x lt 5 000000009 x 10 cos X sin x cos x x lt 1 tanx 3x x
5. and DRG The calculator will display the value of t1 3 141592654 value of 180 in radian 7 Addition Multiplication Subtraction and Division a Addition of Two Numbers Example 8 5 Key to Press Display ION C 0 8 8 8 5 5 13 b Multiplication Division and Subtraction of Two Numbers These calculations are performed in the same manner as the addition 8 Constant Calculations In the constant calculations the addend becomes a constant Subtraction and division are performed in the same manner For multiplication the multiplicand becomes a constant Example Key to Press Display ION C i 122 109 16 x 36 180 9 Trigonometric Functions The functions cosine sine and tangent are accessed respectively by the keys cos sin and tan To calculate for example the cosine of an angle enter the value of the angle and press the key cos Example The calculation cosine of 60 make sure the calculator is In degree mode
6. n Number of samples rx Sum of samples x data rx Sum of squares of samples x data Example Analyze the sample 67 55 51 100 87 89 60 82 Key to Press Display ION C 0 2ndF STAT 0 STATmode 6 7 DATA i 5 5 DATA 2 5 1 DAT 3 1 0 o DATA 4 8 7 DATA 5 8 9 DAT 6 6 0 DAT 7 8 2 DAT 8 x 73 875 2ndF ox 16 84070589 n 8 PndF gt x 591 2ndF gt x4 45929 sx 18 00347189 x 324 125 a Data entry and Correction Entered data is kept in the memory until 2ndF STAT or OFF is pressed Before entering new data clear the memory contents 1 Data Entry Data DATA Data x frequency DATA To enter multiples of the same data 2 Data Correction Correction prior to pressing DATA Delete incorrect data with ON C Correction after pressing DATA Reenter the data to be corrected and press 2ndF ICD The number displayed after pressing DATAjor 2ndF ICD during data entry or cor
7. lt 10100 Inx logx 0 lt x lt 10100 ex 10100 lt x lt 230 2585092 10x 10100 lt x lt 100 sinhx coshx x lt 230 2585092 tanhx x lt 10100 sinh x x lt 5X 1099 cosh x 1 lt x lt 5X 1099 tanh x x lt 1 x2 x lt 1050 vx 0 lt x lt 10100 1 x x lt 10100 x 0 n 0 lt n lt 69 gt D MS x lt 1X 10100 DEG xyore xl lyl lt 1050 x2 y2 lt 10100 0 lt r lt 10100 DEG e lt 4 5x1010 r O4xy RAD e lt 785398163 3 crab 6 lt 5x1010 DEG gt RAD GRAD gt DEG DRG Ix lt 10100 T RAD gt GRAD x lt 1098 sy gt 0 10 lt xIny lt 230 2585092 y 0 O lt x lt 10 ey lt 0 x n y 1 0 lt x lt 1 21 1 x 0 10 lt xIn y lt 230 2585092 sy gt 0 10 Iny lt 230 2585092 x 0 y 0 O lt x lt 10 vy ey lt 0 x 2n 1 1 O lt x lt 1 5 n x 0 1 10 lt zInly 230 2585092 A Bi C Di A C lt 10 A Bi C Di B D lt 10 AC BD 100 Sa _ C2 b2 lt 10 A Bi C Di BCAD an C2 D2 C D 0 DEC x lt 9999999999 BIN 1000000000 lt x lt 111 1111111 OSxS111111111 OCT gt DEC 4000000000 lt X lt 777 gt BIN 7777777 7 OCT 0 lt x877777777 HEX 7 HEX FDABF41C01 lt X lt FFFFFFFFFF 0 lt x lt 2540BE3F F x n integer Specifications Display capacity 10 digits in full floating or 8 digits mantissa with 2 digit and 2 exponent Power Supply LR1130 1 1 5V Power C
8. Aurora Operating Manual For use with AX 501 Single line scientific calculator Printed in China 9220230 Introduction AURORA AX 501 calculator The AURORA AX501 is a calculator with simplicity of use and many capabilities that will appeal to both professionals and student alike It allows you to perform all elementary calculations has a memory and the most commonly used trigonometric and logarithmic functions as well as calculations in binary octal or hexadecimal number bases Removing and Replacing the Calculator s Cover Always slide the keyboard end of the unit into the cover first Never slide the display end of the unit into the cover Holding the cover as shown in the illustration slide the unit out of the cover before use Picture 1 Holding the cover as shown in the illustration slide the unit out of the cover after use Picture 2 Precautions Don t expose the machine to water direct sunlight extremely hot or cold temperatures or dusty environments Don t drop the machine or subject it to heavy impact Use a soft cloth to clean the machine Do not use detergents Never dispose of batteries in a fire Keep batteries out of the reach of children Press the RESET switch on the front with the tip of a ball point pen or similar object only in the following cases Do not use an object with a breakable or sharp tip Note that pressing the RESET switch erases all data stored in me
9. Press Display ION C 0 5 LJL7 5 7 hyp 5 7 cos 149 4353735 9 114 9 4 l2ndF 9 4 larc hyp 9 4 sin 2 936674272 8 7 8 7 hyp 8 7 an 0 999999944 13 Percentage Calculation The second function of the key marked by permits percentage calculations We can sum up the capabilities of this function in four examples Key to Press Display ION C 0 3 7 0 370 x 370 5 0 50 2ndFI 50 Ao 0 5 185 14 3 5 135 Zi 135 2 5 10 250 l2ndF 250 Ao 2 5 54 2 3 0 230 230 2 0 20 l2ndF 20 Ao 46 276 1 8 0 180 180 5 0 50 l2ndF 50 Ao 90 90 14 Exchange Key During calculation the calculator files the information in different registers or reserve the numbers in the number register that we will call the x and y later and the sign of the operation in the sign register Key to Press Display Explain The registers x ON C 0 and y contain 0 The registers y 8 8 contain 8
10. for the execution of subtraction in order to perform the multiplication When you press the key _ the small sign appears on the display above the digits means that parenthesis has been opened This sign disappears when the parenthesis is closed b Levels of the Parenthesis There are 4 levels of parenthesis This means that you cannot have more than 4 operations pending Try the calculation 2 3 4 5 6 7 To carry out this calculation simply press the keys in the order they appear in writing When you press the fifth sign the error message will display c Closing Parenthesis Instead of closing the nested parenthesis and pressing the key simply press the key and calculator will give the correct result For example in the calculation of 5x 4 9 you type 5 x 4 19 Ls instead of 5 x 4 1 19 you will get the correct answer 5 Selecting the Display Notation and Decimal Places When calculation result is displayed in the floating point system pressing FE displays the result in the scientific notation Pressing FE once more displays the result again in the floating point system Pressing 2ndFj TAB and any value between 0 and 9 specifies the number of decimal places in the calcula
11. l system 22 Complex Number Calculations To carry out addition subtraction multiplications and division using complex numbers press 2ndF CPLX to select the complex number mode A complex number is represented in the a bi format The a is the real part while the bi is the imaginary part When inputting the real part you should input the number before press a When inputting the imaginary part you should input the number before press b To obtain the result press Immediately after completing calculation you can recall the value of the real part with a and the value of the imaginary part with b If the complex numbers are represented as polar coordinates press 2ndF xy the numbers are input with a and b Example 12 6i 7 18i Key to Press Display ON C 0 endF CPLX 0 CPLX mode 1 2 a 6 b 6 7 La ft 8 b 18 19 bj 12 23 Statistical Calculations Press 2ndF STAT to select statistics mode The following statistics can be obtained x Mean of samples x data sx Sample standard deviation x data Population standard deviation x n data
12. lected HEX Indicates that 2ndF HEX has been pressed Hexadecimal system mode is selected CPLX Indicates that 2ndF CPLX has been pressed Complex number mode is selected STAT Indicates that 2ndF STAT has been pressed Statistics mode is selected M _ Indicates that a numerical value is stored in the independent memory E Appears when an error is detected Before Using the Calculator Key Notation Used in This Manual In this manual key operations are described as follows A T TO specify A HEX A TO specify m 2ndFj 1 TO specify Exp Exp Functions that are printed in the same colour as l2ndF above the key require 2ndF to be pressed first before the key Numbers keys do not have second unction regardless of pressing 2ndF first but as ordinary numbers B Operating Instructions 1 Power On and Off Press ON C to turn the calculator on and OFF to turn it off 2 Clearing Numbers Press ON C to clear the entries except for a numerical value in the independent memory and statistical data Press CE to clear the number entered prior to use of function key Incase of one digit correction of the entered number press right shift key
13. mat express in degrees minutes seconds into a decimal format in degrees key 20 Coordinate Conversions It may be of interests to convert between polar coordinates r 8 and rectangular coordinates x y To perform the conversion follow the steps below 1 To input the coordinates to be converted enter the first coordinate x or r then the key a and the second coordinate y or then key 2 Press 2ndF xy for polar rectangular conversion or 2ndF gt r for rectangular polar conversion o EA 3 The first coordinate of the result is display second coordinate of the result is obtained with the key b Example x y 1 2 into polar coordinates Key to Press Display ION C 0 1 La 1 2 b 2 2ndF I 2 gt r 2 236067978 bj 63 43494882 21 Binary Octal Decimal and Hexadecimal Operations N Base This calculator can perform the four basic arithmetic operations calculations with parentheses and memory calculations using binary decimal and hexadecimal numbers When performing calculations in each system first set the calculator in the desired mode before entering numbers It can also perform conversions between numbers expressed in binary octal decimal and hexadecimal systems Conversion to each system is performed by the following Keys l2
14. mory When using for the first time After replacing the batteries To clear all memory contents When an abnormal condition occurs and all keys are inoperative Display Floating point system 2ndF HYP DEG RAD GRAD BIN OCT HEX lt Symbol e ic 3450090 E I OU Scientific notation system a HYP DEG RAD GRAD BIN OCT HEX Fob 1 99 _ Mantissa Exponent During actual use not all symbols are displayed at the same time If the value of mantissa does not fit within the range 0 000000001 9999999999 the display changes to scientific notation The display mode can be changed according to the purpose of the calculation 2ndF Appears when 2ndF is pressed indicating hat the functions that are printed in the same colour as l2ndF are enabled HYP Indicates that hyp has been pressed and he hyperbolic functions are enabled If 2ndF jarc hyp are pressed the symbols 2ndF HYP appear indicating that inverse hyperbolic functions are enabled DEG RAD GRAD Indicates angular units and changes each time DRG is pressed The default setting is DEG Appears when a calculation with parentheses is performed by pressing BIN Indicates that 2ndF BIN has been pressed Binary system mode is selected OCT Indicates that 2ndF OCT has been pressed Octal system mode is se
15. ndF BIN Converts to the binary system BIN appears l2ndF OCT Converts to the octal system OCT appears HEX appears 2ndF DEC Converts to the decimal system BIN OCT HEX disappear from the display Note Normally you should keep the calculator in the decimal mode Some of the calculator s features are operative only in the decimal mode Examples 1 Convert 35 decimal to binary octal and hexadecimal numbers 2 Convert 2F hexadecimal to decimal number 3 What is the negative complement number of 63 octal 4 1001 11011 100100 binary 5 2434 decimal 1CF hexadecimal 36 octal 4621 octal 2449 decimal NO Key to Press Display ION C 0 l2ndF gt DEC 3 5 35 i l2ndF 4 BIN 100011 l2ndF OCT 43 l2ndF gt HEX 23 3 l2ndF gt HEX 2 FI 2F l2ndF gt DEC 47 3 l2ndF gt OCT 6 3 63 7777777715 PndF PBIN 1 0 0 fi 4 AAE 100100 l2ndF gt DEC 2 4 3 AIl l2ndF gt HEX 1 C FI 2434 5 1CF l2ndF gt OCT 3 6 36 m 4621 l2ndF gt DEC 2449 2ndF HEX Converts to the hexadecima
16. onsumption 0 00037W Usable temperature 0 40 C Size L144xW75xH10 mm Weight 71 g hard cover not included Producer Aurora Electronics UK LTD Unit 1 amp 2 Shires Industrial Estate Lichfield Staffordshire WS14 9AZ U K
17. rection is the number of samples n b Statistical Calculation Formulas 2 awe xu ox Zx n n x nx n 1 X X X Xz Xn 2 2 2 Ex X X X te Xn In the statistical calculation formulas an error will occur when The absolute value of the intermediate result or calculation result is equal to or greater than 1x10 The denominator is zero An attempt is made to take the square root of a negative number 24 Errors An error will occur if an operation exceeds the calculation ranges or if the wrong mathematical syntax is attempted In the case of an error the display will show E An error can be cleared by pressing ON C 25 Battery Replacement Notes on Battery Replacement Improper handling of batteries can cause electrolyte leakage or explosion Be sure to observe the following handling rules Make sure the new batteries are the correct type When installing orientate the battery properly as indicated in the calculator When to Replace the Battery If the display becomes dim and has poor contrast replace the battery Replacement Procedure 1 Turn the power off by pressing OFF 2 Remove two screws Fig 1 3 Lift the battery cover to remove 4 Remove the used battery then replace with one fresh battery with the positive side facing up Fig 2 5 Replace the battery cover and screws 6 Press the RESET switch on the front
18. tion result To clear the setting of decimal places press 2ndF TAB Example 1 3 Key to Press Display ION C 0 1 1 1 3 3 floating point 0 333333333 2ndF 0 333333333 an 0 333333333 2 0 33 FOE 3 33 01 F E 0 33 2ndF 0 33 TAB 0 33 O 0 333333333 If the value for floating point system does not fit in the following range the calculator will display the result using scientific notation system 0 000000001s x s9999999999 6 Angle Units Degree Radian and Gradient Before any trigonometric calculation make sure the angle unit with which you use to make the calculation conforms with the one that the calculator will use The angle unit is indicated above the display of the digits This unit is marked by DEG for degree RAD for radian and GRAD for gradient Each press the key DRG will alternate between these units You may also want to convert an angle into another unit The function that enables you to do that is the second function of the key DRG marked IDRGP We shall try to convert 180 in radian First make sure that the angle unit display is the degree symbol DEG Press the number 180 then press the key 2ndF
19. y key RCL recall the content of the memory to the display key M adds the displayed number to the memory with this sum I DEG and vice versa with the second function of the key DEG marked by D MS For example the conversion of 1 876543203 into degree minute second Example Key to Press Display ION C 0 1 18171615 41 3 2 0 8 1 876543203 2ndF 1 876543203 You must read D MS 1 523555 1 52 35 55 DEG 1 876543203 Example Key to Press Display ION C 0 8 8 x 8 2 2 16 ISTO 16 2 14 M 24 RCL 40 18 Chain Calculations This calculator allows the previous calculation result to be used in the following calculation The previous calculation result will not be recalled after entering multiple instructions Example Key to Press Display ION C 0 4 5 45 45 14 6 16 61 61 7 7 68 19 Time Decimal and Sexagesimal Calculations This calculator also makes it possible to convert an angle from sexagesimal for
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