Last term's first midterm

This is a copy of the first midterm given in the Fall 1993 CSCI 254 that I taught. Problems 1, 3, and 6 are from Chapter 1 of the text book while problems 2, 4, and 5 are from Chapter 2. This was an open book exam.

Problem 1. (15 points)

Show how to simplify the Boolean expression (ABC'+C)(A+C) to be A B + C using Boolean algebra.

Problem 2. (10 points)

The contents of an eight-bit shift register is initially 00110110. The register is shifted left three times with the serial input being 010. What is the contents of the shift register after each shift?

Problem 3. (15 points)

What is the value on the Q' output of the JK flipflop in the following diagram after the circuit is clocked (using the clock input, of course) for the third time?

J K flip-flop

Problem 4. (15 points)

Show how to construct a 4-to-1 multiplexer from three 2-to-1 multiplexers.

Problem 5. (15 points)

Suppose you are given a 1G x 16 bit ROM chip.

How many address input lines does the chip have?
How many data input lines does the chip have?
How many data output lines does the chip have?
How many bytes are stored in the chip?

Problem 6. (30 points)

A sequential circuit with two inputs x and y, a single output z, and one D flip- flop A is described by the following equations.

z = A + x y
DA = A' +x'

Suppose you have to recreate the circuit, but using a JK flipflop rather than a D flipflop. What are the logical functions you'd use to compute JA and KA?