CSE 370 Laboratory Assignment

Introduction to Registers

Assigned: Monday, February 15, 2010
Due: End of Lab Section

Objectives

The objective of this lab is to introduce you to edge-trigged D-type flip-flops as well as linear feedback shift registers. You can refer to Chapter 6 of your textbook Contemporary Logic Design for more information. Typically for flip-flops and registers you use a clock signal, however, a typical clock signal such as ones provided one your hardware are far too fast for the LED changes to be visible to the unaided eye – they are just too fast.  Therefore, we will simulate clock pulses throughout this lab by using a button. Even though a button is not a regular clock, what happens when the button is depressed is roughly the same; a pulse is sent through the circuit with both negative and positive edges that will be used to trigger flip-flops. You can consider button pushing to be a very slow irregular clock signal – but one that you can control.

 

Before You Begin

If you followed the instructions properly in the previous lab, when you turn on your board for this lab you will notice that the original program loaded on the FPGA is still there, which means you can make use of the switches, LEDs and buttons directly connected through the input/output connectors on the board. If you find that this is not the case, call over a TA and they will assist you in restoring your old settings. Of course, by now, you are well versed in the FPGA, which means you can undertake the task of rerouting the switches, LEDs and buttons yourself if you choose to.

 

Part 1: D Flip-Flops

Tasks:
  1. The '74 package has 2 D flip-flops. You'll note each flip-flop has a data input, D, a clock input, CP, two outputs, Q and Q', and two additional inputs, SD and CD. These last two are active-low (they have an effect when 0 and none when 1) asynchronous set and clear inputs. Insert the '74 chip into your breadboard and connect the D input to one of the switches, a button to the clock input, and Q to one of the LEDs. Make sure to also connect SD and CD to a logical 1, such as VDD to ensure that they aren’t triggered for this first part.

  2. Spend some time experimenting with the flip-flop. Toggle your switch so that a value of 1 is on the D input to your flip-flop and press the button. What happens to the LED you connected to Q? Try changing the value of D and push the button again. Try changing D back and forth while not pushing the button wired up as your clock. Note how Q only changes after you press the push button. This is a synchronous flip- flop, changes in the output only occur after a rising clock edge (positive edge-triggered, this occurs every time you press the button down because the button generates a positive pulse). You can surmise that if you had a faster clock, such as someone pushing the button for you very quickly, whenever you flipped the switch the effect would appear almost instantaneously, depending on the speed of the clock.

    Clock Skew

    We will experiment with clock skew by using even numbers of inverters to delay the propagation of your simulated clock.  Wire up the second D flip-flop on the ’74 package. Use your output from the first flip-flop as the input for the second flip-flop. Also, wire the same button to both clock inputs. Your circuit is now a 2-bit shift register. Try shifting in some bits; because both flip-flops’ clocks are in sync, it will function as expected. Now, add a ’04 inverter package to your breadboard and wire together two of the inverters in a chain.  Connect the clock button to the clock input of the first flip-flop and to the input of the first inverter in the chain. Connect the inverter output at the end of the inverter chain to the clock input of the second flip-flop. The two inverters’ delay will now skew the clocks received by the two flip-flops.  See if your shift register still works.  Does it still work if you add two more inverters to the inverter chain, for a total of four inverters; skewing the second clock signal even further?  What does this mean about the relationship between the delay of the inverters and the timing constraints of the flip-flops?  Show your TA a case where the two-bit shift register functions as expected and a case where it does not work due to clock skew.

  3. Now it is time to experiment with the asynchronous set and clear inputs. Connect these to switches instead of VDD (logic 1) to which they were previously connected. Make sure the switches are initially set to output a 1. Now, set the value of Q to 0 using the D input and the push-button. Flip the SD switch. What happens? Did you have to press the push-button? Asynchronous input take effect immediately, without waiting for the next clock edge. Repeat the experiment with CD instead of SD. Try setting both SD and CD to 0 (set and clear at the same time), which dominates? Does the flip-flop set or clear?

  4. Copy the timing diagram below onto your own piece of paper and fill in the rows for Q and Q' for the first check-off.


Part 2: Linear Feedback Shift Registers (LFSRs)

LFSRs have an interesting property that a particular function of a subset of the outputs will cause the shift register to cycle through a maximal length sequence of output values. In the case of a 4-bit shift register, a maximal length sequence would have 15 (16 - 1, the all-zero pattern is not counted) different outputs. If the function can be implemented efficiently, this capability can be much easier to implement than building a binary counter (recall that a binary counter is a specialized adder but still has a long carry-chain of larger and larger gates).

Binary counters with a large number of bits can be quite expensive in terms of the logic they require. On the other hand, LFSRs with maximal sequences can be made with input functions that are low fan-in (depend on only a few of the register's outputs) and do not have a carry-chain. This makes LFSRs very attractive when we need to count to large values but don't care about what the patterns are (that is, they don't have to be consecutive binary numbers). Variations of LFSRs are often used as random number generators as well - consecutive output patterns can be made to look quite different and are uniformly distributed over the space of all possible patterns. You can read a lot more about LFSRs at Wikipedia : each of these sites includes a complete list of functions that will generate maximal sequences for any number of bits from 4 to 32 and beyond.

For example, a 4-bit LFSR with maximal length sequence will have the following function: D1 = Q4 xor Q3. A larger 8-bit LFSR with D1 = Q8 xor Q7 xor Q6 xor Q1 will have a 255 pattern long maximal sequence. Interestingly, a 32-bit LFSR can also have a maximal sequence (232-1 patterns long) with a function of only 4 output variables, namely, D1 = Q32 xor Q31 xor Q30 xor Q10.

Tasks:
  1. Wire up your '377 octal D-FF to form a 4-bit shift register. Connect the four FF outputs to four of the LEDs. Connect the output of a 2:1 multiplexer to the first input with a switch connected to the mux's control input. The two mux inputs should be the value of another switch and the last output of the shift register (the fourth bit). Verify the operation of your shift register by setting the input to come from the switch. Go through a few clock cycles shifting in different values. Make sure to tie the enable input of the '377 to a value rather than leaving it floating as it may not function properly without a valid logic level on that input. Show your shift register to a TA for the first part of the second check-off.

  2. Shift the pattern 1, 1, 0, 0 into your shift register. Flip the input mux switch so that the last output is now fed back into the input. Go through a few clock cycles by pressing the button you have wired up as your "clock". You should see your pattern shifting in a circular pattern through the register. How many different patterns are there in all before the output pattern on the LEDs repeats itself?

  3. Invert the value of the last bit being fed back around before it goes into the mux. Repeat the previous task with this new configuration. How many different patterns do you see?

  4. Remove the inverter and replace it with an XOR gate with the 4th and 3rd FF outputs as its inputs. Connect the output of this XOR gate to the input mux of the shift register. This is a 4-bit LFSR. Begin by shifting in zeros into your shift register (use the switch input to the mux). Now flip the mux to select the output of the XOR gate to be the input. Go through a few clock cycles. Does the pattern change? Now, shift in all ones (instead of zeros) to set up the shift register and then go through a few clock cycles. How many patterns do you go through before they begin to repeat? Is this a maximal sequence? Show your LFSR in operation to one of the TAs. Try different taps instead of 4th and 3rd, for example, 4th and 2nd. How many different patterns does this configuration generate? Demonstrate your LFSR to the TA to second part of the second check-off.

Lab Demonstration/Turn-In Requirements

A TA needs to "Check You Off" for each of the tasks listed below.

  1. Demonstrate the effect of clock skew on your register in Part 1, Task 2.
  2. Show your completed timing diagram from Part 1, Task 4.
  3. Demonstrate a.) your 4-bit shift register from Part 2, Task 1 and b.) LFSR from Part 2, Task 4.

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