ECE 275: Digital Design I
Class 15Universal Gates
2 Universal Gates
- NAND
- NOR
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
- 8:1 MUX with 3 select lines
- 16:1 MUX with 4 select lines
- 32:1 MUX with 5 select lines
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))'