Quiz 1 -- 19 February, 1995

This is an open book, open notes exam. It is to be turned in by 5:30 PM.

Problem 1. (17 points)

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

• x(x' + y x)
• x y
x y your stuff goes here 0 0 0 1 1 0 1 1

Problem 2. (17 points)

Simplify the following Boolean expression using Boolean algebra.

• x(y' + z y + y) + z'

Problem 3. (17 points)

Simplify the following Boolean function using a Karnaugh map. Notice the "don't care" conditions. Be sure to write your answer as a minimal sum-of-products Boolean Function.

• F(x, y, z) = Sigma(0, 3, 4, 6)
• F(x, y, z) = d(1, 5)

Problem 4. (17 points)

What would the espressoinput for the Boolean described in Problem 3 look like? (Start with the following.)

```.i 3
.o 1
.ilb x y z
.ob F
# it's all yours from this point on
```

Problem 5. (17 points)

What is the Boolean function computed by the following circuit?

Express your answer by completing a truth table corresponding to the circuit.

x y z
00
01
10
11

Problem 6. (15 points)

How should the Jand Kinputs of a JK flip-flop be set to make the output of the flip-flop change from 1 to 0 on the next clock cycle?

How should the J and K inputs of a JK flip-flop be set to make the output of the flip-flop be 1 on the next clock cycle regardless of the present output?