# Last semester's first test

This is a copy of an open books, open notes exam that was given as the first test in CSCI 254 in the Spring 1994 semester. By the way, this exam was too easy.

## 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    J-A   K-A    J-B   K-B
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.