Flip-Flops and Frequency Division
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1. be counting 0 1 2 3 over and over again TODO Once you have it counting to 3 show it to your TA 5 Frequency Division and Counting Our Magic Boxes only have one clock wave generator each if we want to make a counter with one Magic Box we need to be able to get multiple clock wave frequencies out of one generator We accomplish this by making a frequency divider It is a circuit which takes in a wave and outputs a wave that is half as frequent high input low high output low time We can make a frequency divider with one flip flop like so clock Thanks to the physics of these integrated circuits no D input is needed to get the circuit to work If you connect both your clock signal and the output of your frequency divider to your number display you should get it counting 3 2 1 0 repeatedly Check to see that s what happens To get your circuit to count upwards invert your original clock signal clock f o LED You should be seeing it count 0 1 2 3 repeatedly we call this a 2 bit counter TODO Show your 2 bit counter to your TA Now build a second frequency divider with a different LS175 chip Verify that it works You can now build a circuit that repeatedly counts up to 7 using both of your frequency dividers You might want to figure out how you want to connect the two together on paper beforehand since you will have to figure out which inputs and outputs go togethe2. can be read simultaneously A different type of shift register is a parallel in serial out PISO shift register In a PISO shift register data bits are loaded in simultaneously and then the stored data can be shifted out of the register and read serially one bit at a time Shorthand for the PISO shift register is illustrated on the left below and for the SIPO shift register on the right outputs input output PISO shift register SIPO shift register Consider the following problem A student tries to make a 4 bit parallel to serial to parallel circuit with this in mind Input output But the student gets stuck on how to clock the circuit after coming up with the following After precisely 4 clock cycles have completed and before the 5th clock cycle begins the student wants W to output the value of A X to output the value of B Y to output the value of C and Z to output the value of D In Logisim connect up the dangling wires so that the circuit works as intended To get the bonus mark you must be able to explain what each part of the circuit above is doing as you clock it Download the file piso_sipo circ from the course website and load it in Logisim It might be helpful to set initial values for A B C and D for example A 1 B 0 C 0 D 1 and track how the values are passed along the circuit Note that in Logisim the D input for a flip flop is on the lower left and the clock input is on the upper left To reset
3. CPSC 121 Models of Computation Lab 5 Flip Flops and Frequency Division Objectives In this lab you will be introduced to two types of circuits called latches and flip flops Latches and flip flops can be used to store information this is useful when a system s current output depends on one or more of its previous outputs You will also be working with different clock frequencies and using them to make 2 bit and 3 bit counters 1 Pre lab 1 1 Counting Notice that there is a parallel between binary numbers and truth tables and a pattern can be seen in both The right most column repeats 01010101 the one immediately to the left repeats 00110011 the next one repeats 00001111 and so on In circuits if we want to repeat a pattern like this we use an electrical wave like the clock output on the Magic Box which regularly alternates between 0 and 1 at a set frequency Using the three waves in the figure below we can produce the same pattern and repeatedly count up to 7 wave oP Lo fsbo fz lefile wave wave number 0 1 2 3 4 5 6 7 0 What differs between the three waves is their frequency waveo is twice as frequent as wave which is twice as frequent as waveg If we want to be able to count up to 15 all we need to do is add another wave which is half as frequent as wave2 Have a look at this animation which has such a wave Recall that 1 Hz means once every second 2 Hz means twice every seco
4. be the value of the latch s output q 5 Lastly after that suppose we switched en 0 What would be the value of the latch s output q 1 3 Flip Flops A flip flop is another type of sequential circuit and is very similar to a latch However when the flip flop will load in a new value is different With the latch we took in a new value whenever en was on so if we left en on and flipped d on and off we would see q go on and off in response Flip flops only take in a new value when en becomes on Once en is on nothing changes we have to turn en off and then on again to load in a new value Because of this en is typically connected to a clock wave this allows it to regularly load in new values A new value is loaded every time the clock wave becomes on otherwise we hold onto the old value We represent flip flops with this symbol In the flip flop D is our input Q is the value we re remembering and gt represents the clock input replacing the en of the latch TODO pre lab What is the Q output Look this up and cite your source If you are searching on the internet it will help to look for a D Flip Flop 2 A Flip Flop Connect up a 74LS175 Quad D Flip Flop chip to power and ground on a Magic Box Then power the Clear input in the lower left corner of the chip Clear can be read as not Clear The complement or inversion of a signal is typically written with a line over top For one of the four flip
5. flops in the circuit connect 1D to a switch 1Q and 1Q to LEDs and CLOCK to a connection in the clock output box Figure 1 The clock output box of a Magic Box Unlike in Lab 1 where we used a clock wave that was generated by the Magic Boz here we want to use a manual clock there is a white button above the clock output that you can press it s at the top in the fig ure above Each time you press the button a new clock cycle begins the clock begins outputting a value of 1 when you release it the clock cycle is complete the output of the clock again becomes 0 For how to switch to manual clocking see page 6 of the Magic Box User s Manual TODO Determine a truth table for this circuit For some entries you may want to define and use variables like qprev or describe what happens in English D Goa butim 0 7 _ of spewed af sws OP 0 is not pressed P 1 is not pressed PoP 3 Shift Registers Flip flops can be connected together so that their states can be passed down a chain This is called a shift register Using your D Flip Flop connect 1Q to 2D and 2Q to 3D to connect three flip flops in a chain Also connect 1Q 2Q and 3Q to green yellow and red LEDs respectively Keep the clock connected to the clock button and 1D connected to a switch Figure 2 shows a diagram of the circuit you are implementing LED LED LED Figure 2 Three flip flops connected in series TODO Test your circuit to see w
6. hat happens Play with different values for 1D and see what happens as you clock the circuit manually What happens 4 Wiring a Counter In this section you will wire up a 2 bit counter with two Magic Boxes 1 Find another team that has a Magic Box 2 Turn off the power to the Magic Boxes while wiring them together 3 Leaving your original power and ground wires still connected connect the ground input of one Magic Box to the ground input of the other one This gives the two circuits a common reference for voltages Do NOT connect the power signals together Each Magic Box has its own voltage regulator that converts 9 volts from the AC power adapter to 5 volts for the breadboards While the output voltages are very close to 5 volts there will be slight differences between the boards If you connect the outputs of two voltage regulators together they can fight over what the right output voltage is This violates the specification for how the regulators are supposed to be used and could lead to a malfunction 4 One team should set their Magic Box s clock frequency to 1 Hz and the other team should set theirs to 2 Hz See page 6 of the Magic Box User s Manual for how this is done 5 Now connect the 2 Hz clock wave to the rightmost LED on your board it is orange and labeled BO 6 Connect the 1 Hz clock wave to the LED beside it it is green and labeled B1 7 Turn on your Magic Boxes and look at the number display It should
7. nd etc TODO pre lab If we wanted the animation to count to 31 what frequency in Hz would wave have 1 2 Sequential circuits Here s another way of thinking about counting Consider the mathematical formula tn tn 1 1 where to 0 Here we re taking the previous value of t and using it to get the next one For example ti to 1 0 1 1 b l gt r Notice how the value of tn depends on tn 1 the value that comes before it This type of behavior can also be seen in circuits When we store and use the previous output of a system we call it a sequential circuit A latch is a type of sequential circuit which works like this e If en 0 the latch s output q is its previous output dprev e If en 1 the latch s output q is its input d The latch allows us to remember a value it is a simple form of memory It looks like this The truth table for this circuit differs from ones you ve seen before now we have a variable qprev representing the latch s previous q value TODO pre lab Answer the following questions 1 Suppose we turned on the latch with en 1 and d 0 What would be the value of the latch s output q 2 Now suppose we after doing that step above switched en 0 What would be the value of the latch s output q 3 And now after that step suppose we switched d 1 What would be the value of the latch s output q 4 Now after that step suppose we switched en 1 What would
8. r If you get stuck ask your TAs for help TODO Show your 3 bit counter to your TA once you have it working 6 Further Analysis Questions TODO further analysis Because sequential circuits take their outputs as an input they typically start off having an undetermined state When does a flip flop have a determined state and what could some problems of having an undetermined state be 7 End of Lab Survey TODO To help us improve these labs both this term and for future offerings complete the survey at http www tinyurl com cs121labs 8 Magic Box cleanup TODO Before leaving the lab show your Magic Box to your TA A Challenge Problem Serial communication is the process of sending data one bit at a time while parallel communication is capable of sending multiple bits simultaneously A simple illustration can clarify the difference In this lab we showed you a serial in parallel out SIPO shift register LED LED LED switch clock Figure 3 Three flip flops connected in series with parallel outputs As there are three bits of memory in this shift register one in each flip flop we call this a 3 bit SIPO shift register Shift registers are used for the storage or transfer of data and can be used to convert data either from a serial to parallel format or vice versa In a SIPO shift register data is loaded in serially one bit at a time This stored data is then available in parallel form all bits in the register
9. the circuit press Ctrl R B Marking scheme All labs are out of ten marks Two marks for pre labs and eight marks are for in lab work Two marks Pre lab questions Five marks In this lab it is 1 point for Section 2 flip flop 1 point for Section 3 shift registers 1 point for Section A wiring a counter and 2 points for Section 5 frequency division counters One mark Further analysis One mark End of lab survey One mark Magic Box cleanup TAs may at their discretion award one bonus mark such as for completing a challenge problem
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