Exam ID: 1522

1. Which of the following best describes the difference between combinational logic circuits and sequential logic circuits?

1. Combinational circuits all have a clock input, but sequential circuits never do.
2. Sequential circuits all have a clock input, but combinational circuits never do.
3. Combinational circuits always produce the same output values for a given combination of input values, but sequential circuits can produce different output values for a given combination of input values.
4. There is no difference between combinational and sequential logic circuits.
5. Sequential circuits don’t use NOR gates.

2. What is the period of a 1.25 GHz clock? (Hint: the following answers are listed in decreasing numerical order from A to E.)

A. 800 milliseconds

2. 800microseconds
3. 800 nanoseconds
4. 800 picoseconds
5. 800 femtoseconds

3. What is the frequency of a clock with a period of 125 nanoseconds? (Hint: the following answers are listed in increasing numerical order from A to E.)

A. 8 Hz

2. 8 KHz
3. 8 MHz
4. 8 GHz
5. 8 THz

4. What determines the maximum clock rate of a CPU?

A. The maximum number of propagation delays in the datapath.

2. The average number of propagation delays in the datapath.
3. The minimum number of propagation delays in the datapath.
4. The total number of registers in the datapath.
5. The average fan-out of each gate in the datapath.

5. Using full adders as building blocks, draw a four-bit parallel adder/subtracter with condition code logic for carry, overflow, negative, and zero. Label all inputs and outputs. Do not draw the gates for the full adders. See Question 6 for the labels you should use for inputs and outputs. Answer on the back of this page.

6. Complete the following diagram for the adder/subtracter you designed in Question 5. For add/sub, 0 means add. C, V, N, and Z are the condition code bits Carry, oVerflow, Negative, and Zero. You are to fill in zeros and ones for the 8 outputs on the right given the nine input values on the left. Answer here:

A3	A2	A1	A0	B3	B2	B1	B0	add/sub	C	V	N	Z	S3	S2	S1	S0
0	0	0	0	0	0	0	0	0
0	1	1	1	0	0	1	0	0
1	1	1	1	1	1	1	1	1
0	0	1	1	0	1	0	1	1

7. Give the equation for C₅ using carry-lookahead logic. Write your answer here:

8. Draw the gates to implement both a D Latch and a D flip-flop. Be sure to label all inputs and outputs for both. Answer on the back of page 1.

9. Complete the following timing diagram for the latch and flip-flop you drew in Question 8: The idea is that Clock and D are the same for both the latch and the flip-flop and you are to show the outputs of both devices, which are both initially 0. The dashed lines are to help you line things up. Answer here.

Clock

D

Q_latch

Q_flip-flop

10. Design a circuit which has two inputs named count and load, and an output named zero. The circuit can be in any of sixteen different states; there is a 4-bit state register named S. When load is one the circuit loads a value into S from an external 4-bit source called Value. When count is 1, S is decremented by one The zero output is 0 (false) except when S holds the binary number 0000₂. You may assume that count and load will never be true at the same time. When neither count nor load is true, the circuit is to do nothing. Answer on the back of this page.

11. Show the binary values of the M, C, A, and Q registers as a 4-bit serial multiplier computes the product of 0110 ´ 1010 using unsigned arithmetic. Indicate what operation is being performed at each step of the multiplication. Answer below.