﻿ Homework

## Week 6 Homework

Due Feb 18

### Problem 1

The seven-segment LED shown below can be used to display any hexadecimal digit. For each of the seven segments there is a four-variable Boolean function that outputs a one when that segment is to be lit and zero otherwise. Generate the truth table for segment 5, write the sum of products expression, simplify the expression using a Karnaugh map, and implement the corresponding circuit using DEEDS.

## Introduction to Problems 2 and 3

A multiplexer has n control lines, 2n input lines and 1 output. When the values of the control lines are interpreted as a number, the corresponding input is passed through to the output.

A truth table describing a binary function of n variables has 2n rows and 1 output column (the function result). When the values of the n variables are interpreted as a number, the desired output is found on the corresponding row of the truth table.

Given the remarkable similarity of a truth table and multiplexer, it should come as no surprise that any binary function of n variables can be implemented using a multiplexer with n control lines. A simple example is shown below. Each input to the multiplexer is the value of the function in the corresponding row of the truth table and the values for A and B select which of these input lines will appear at the output.

In DEEDS, you'll find decoders, multiplexers, and demultiplexers on the component toolbar in the group of components just to the right of the basic logic gates.

### Problem 2

a) Use a multiplexer with 3 control lines to implement the function defined by the truth table below.

b) Use a multiplexer with only 2 control lines to implement this same function. This is a bit more challenging and you'll need to put on your thinking cap. Hint: Connect A to S1 and B to S0. Look for patterns in the pairs of rows that correspond to the different values of AB.

### Problem 3

a) Use a multiplexer with 4 control lines to implement the function defined by the truth table below.

b) Use a multiplexer with only 3 control lines to implement this same function.