ECE 275: Digital Design I

Class 15

Universal Gates

2 Universal Gates

You can use just NAND gates or just NOR gates to make every other gate

NAND Examples

Example: Create inverter with a NAND gate

Example: Create AND using NANDs

Example: Create OR using NANDS

NOR Examples

Example: NOT using NOR

Example: OR using NOR

Example: AND using NOR

Multiplexers (Multiplexor) : Data Selector

Uses an input selector to choose which data goes through

2:1 MUX

When S = 0, F <= A S = 1, F <= B

You can also have 4:1 MUX

Symbol is the same but has 2 selector bits

When S = 00, F <= A S = 01, F <= B S = 10, F <= C S = 11, F <= D

You can also have

MUXes are universal gates

MUX Examples

Example: Inverter using 2:1 MUX

Example: AND using 2:1 MUX

Example: OR using 2:1 MUX

Example: XOR using 2:1 MUX

Example: NAND using 2:1 MUX

Example: NOR using 2:1 MUX

Design Problem: 4:1 MUX using 2:1 MUX's

Design Problem

Program the following 8:1 MUX to implement F = ABC + A'CD + BC'D' + AB'D Inputs: A, A', B, B', C, C', D, D', 0, 1

What should be the values for the pins?

Step 1: Draw the truth table
A B C D F
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 1
0 1 0 0 1
0 1 0 1 0
0 1 1 0 0
0 1 1 1 1
1 0 0 0 0
1 0 0 1 1
1 0 1 0 0
1 0 1 1 1
1 1 0 0 1
1 1 0 1 0
1 1 1 0 1
1 1 1 1 1

Next, figure out select lines For simplicity, make select lines A,B,C

NANDs

NORs

F = A'B + AB' F = ((A'B)'(AB')')' F = ((A + B')(A' + B))'