Quiz 1 -- 20 February, 1995

This is an open book, open notes exam. It is to be turned in by 8:30 PM.

Problem 1. (15 points)

Use truth tables to show that the following two Boolean expressions are equivalent:

z' + x(z + y') + x
x + z'

Problem 2. (20 points)

Simplify the following three Boolean expressions using Boolean algebra.

((x y)' + x)z + (a' + b')'
A B B A + A' + A'(A + A B)
x z + x z' + x'

Problem 3. (15 points)

Simplify the following two Boolean function using a Karnaugh map. Notice that the second function has some ``don't care'' conditions.

F(x, y, z) = Sigma(0, 1, 3, 4, 6)
F(x, y, A, B) = Sigma(1, 5, 6, 11)
F(x, y, A, B) = d(2, 3, 9,14)

Problem 4. (8 points)

Translate the following function

F(x, y, z) = x + y z + z'

into the sum-of-products notation.

Problem 5. (6 points)

Which is the more versatile gate -- the NAND or the OR? Explain your answer.

Problem 6. (6 points)

What happens when a JK flip-flop is clocked when both the J and K inputs are 1?

Problem 7. (30 points)

The following state table is for a finite state machine with a single input x, a single output z, and two state variables A and B. (The four columns on the right are not part of the state table. You will fill those in later.)

x	A	B	z	A	B
	present state			new state
0	0	0	1	0	1
0	0	1	0	1	0
0	1	0	0	0	0
0	1	1	1	1	1
1	0	0	0	0	1
1	0	1	0	1	1
1	1	0	1	0	1
1	1	1	1	0	1

Part A. (8 points)

Suppose two JK flip-flops are used to hold the state variables A and B. Fill in the four columns on the right of the table above for the inputs JA, KA, JB, and KB to these two flip-flops.

Part B. (8 points)

Fill in Karnaugh maps for the JA and KA inputs to the JK flip-flop for A.

Part C. (6 points)

According to the Karnaugh map method of simplifying sum-of-products implementations, what Boolean functions should be used to compute JA and KA?

Part D. (8 points)

Draw the combinational circuits for computing JA and KA. If you can't fit the circuit in this space, you probably have the wrong answer.