# 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` |
`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.

## 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 `espresso`input 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.

## Problem 6. (15 points)

How should the `J`and `K`inputs 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?