E15: Fundamentals of Digital Systems - Fall 2010 - EXAM 2 PRACTICE
1. Analyze this sequential logic circuit.
The circuit below takes as input two 4Hbit binary numbers X and Y, and a 1-bit input EN. It outputs an 8Hbit binary number P. Input to the circuit, but not depicted in the diagram, are a clock line and a reset line, which are both connected to the shift register and to all of the flip-flops. Complete the timing diagram below with traces for the values of A, S, and P (V has already been filled in for you). You can use the space to the right of the diagram for scratch work.
Convert X, Y and the final value of P to their decimal equivalents.
For any numbers X and Y, what would the final value of P be, in terms of X and Y? That is, what function does this circuit compute?
2. Implement a sequential logic circuit to transmit asynchronous 2-E-1 data.
Your circuit should have four inputs: a clock line, a reset line, a 2-bit message D, and a 1-bit input EN. It should have two 1-bit outputs R and Y. Operation for the circuit is specified as follows:
- After a reset, the circuit is in an idle state. The ready-for-data output R is set to 1, and the data output Y is also set to 1. The circuit will remain in the idle state as long as EN is set to zero on a positive clock edge.
- To begin transmitting, the circuit's message input D is set to the desired message, and EN is set to 1. At the next positive clock edge, the circuit leaves the idle state, R is set to 0 to indicate that the circuit is not ready for further input, and Y is set to 0 as a start bit. After the positive clock edge, changing the message input D should not affect whether the circuit correctly sends the message that was originally input.
- For the next 2 clock cycles, R is kept at 0 while Y cycles through the bits of the message that was originally input, from LSB to MSB.
- During the subsequent clock cycle, Y is set to the correct parity bit: 1 if the message contained an even number of 1's, and 0 otherwise. R is still held at 0.
- In the next clock cycle, the circuit returns to the idle state, resulting in setting the data output to 1, and the ready-for-data output to 1 as well.
Draw a logic diagram for your circuit, including any necessary gates and flip-flops. You may omit the clock and reset lines for clarity. Your circuit's outputs should directly depend only on the current state of the flip-flops in the circuit.
3. Latches instead of flip-flops.
Fresh from his fiasco with the soda machine, Bob the digital circuit designer sets out to implement two register circuits: a 4-bit simple register, and a 4-bit PISO shift register. However, he has mistakenly built the circuits with D latches instead of D flip-flops, as in the diagrams below:
Note that the simple register is supposed to store D when X=1, and remain unchanged otherwise. The shift register is supposed to store D when Y=0 and shift to the right otherwise.
Assume that the inputs to the circuit are always set prior to the positive edge of the clock, and are always held until after the negative edge (i.e., the input never changes while the clock is held high). For each of the two circuits:
- Will the circuit work as intended, given the assumption above?
- If so, explain why. If not, draw a timing diagram leading to an incorrect output, and explain why the output is incorrect.