# Homework #1 -- Due September 6

## Problem 1

Simplify the following expressions using Boolean algebra

*x* + *x*' *z* + *y* *z*
- (
*x* + *x* + *x*')(*y* + *z* +
*x*)*x*'

## Problem 2

List a truth table for the following function:

- F(
*A*, *B*, *C*) = *A*' +
*B*'(*A* + *C*) + *C*

Now simply the function using Boolean algebra.

## Problem 3

Simplify the following functions using Karnaugh maps.

- F(
*A*, *B*, *C*, *D*) = Sigma(1, 2, 3, 7,
8, 14)
- F(
*x*, *y*, *z*) = (0, 1, 5, 6)

## Problem 3

Simplify the following functions with don't-care conditions
using Karnaugh maps.

- F(
*A*, *B*, *C*, *D*) = Sigma(0, 1, 3, 7,
11, 12)
- F(
*A*, *B*, *C*, *D*) = d(2, 5)

- F(
*A*, *B*, *C*) = Sigma(1, 3, 5, 6, 7)
- F(
*A*, *B*, *C*) = d(4)

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