# 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.