# 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.)

### 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.