# Midterm 1 -- 24 October, 1995

## Problem 1. (12 points)

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

• (A + B C) (C A' + B)
• A B + B C

## Problem 2. (24 points)

Simplify the following two Boolean expressions using Boolean algebra.

• x + x' y (z + x)
• ( a + b ) (a' + b) c

## Problem 3. (14 points)

Simplify the following Boolean function using a Karnaugh map. Notice the don't care conditions!

• F(x, y, JA, JB) = Sigma(0, 4, 9, 11, 13, 14)
• F(x, y, JA, JB) = d(2, 3, 6, 12, 15)

## Problem 4. (14 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. 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 for the inputs JA, KA, JB, and KB to these two flip-flops.

## Problem 5. (12 points)

• How many address lines are needed for a 4M × 32 ROM?
• How many data input lines are needed for a 8M × 16 ROM?
• How many data output lines are needed for a 16M × 8 ROM?

## Problem 6. (24 points)

Figure 2-5 of the textbook (p. 50), shows a block diagram of a quadruple 2×1 line multiplexor. In the space below, draw a block diagram of a quadruple 4×1 multiplexor.

Now, show how a quadruple 4×1 multiplexor can be implemented with three quadruple 2×1 multiplexrs.

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