# Quiz #1

22 February, 1994

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

## Problem 1. (30 points)

Simplify the following two boolean expressions using Boolean algebra

• A + B(A + C') + BC
• (A + BC)(B + A)

## Problem 2. (20 points)

Complete the truth table for the following Boolean function

• F(x, y, z) = z(x + y'x) + xyz'

## Problem 3. (50 points)

The state table for a sequential circuit with two flip-flops, A and B, and one input x is shown in the five leftmost colums of the following table. (For simplicity no outputs are given even though a sequential circuit with no output is really quite silly.) Fill in the four righmost columns of the table with the appropriate inputs for JK flip-flops implementing these state transitions

```   present state   input       next state
A      B       x          A      B
0      0       0          0      1
0      0       1          1      0
0      1       0          0      0
0      1       1          1      0
1      0       0          0      1
1      0       1          1      1
1      1       0          1      0
1      1       1          1      1
```

Now, derive minimal sum-of-product implementation for the two inputs, JA and KA, to the A flip-flop using Karnaugh maps.

And, finally, in the space below, draw your circuit to compute KA.