1. Multiplexer as a Universal Function Generator
Discussion D4.3

2. Multiplexers s1 s0 C0 C1 4 x 1 MUX Y C2 C3 s1 s0 0 0 C0 0 1 C1 1 0 C2

3. Multiplexers 1 s1 s0 4 x 1 MUX Y s1 s0 =XOR 0 0 C0 0 1 C1 1 1 0 C21 s1 s0 Y 1
=XOR C0 C0 C1 C2 C3 C1
4 x 1
MUX Y C2 C3 s1 s0

4. Multiplexers 1 s1 s0 4 x 1 MUX Y s1 s0 =AND 0 0 C0 0 1 C1 1 0 C21 s1 s0 Y 1
=AND C0 C0 C1 C2 C3 C1
4 x 1
MUX Y C2 C3 s1 s0

5. Multiplexers 1 s1 s0 4 x 1 MUX Y s1 s0 =OR 0 0 C0 0 1 C1 1 1 0 C21 s1 s0 Y 1
=OR C0 C0 C1 C2 C3 C1
4 x 1
MUX Y C2 C3 s1 s0

6. Multiplexers 1 s1 s0 4 x 1 MUX Y s1 s0 =NAND 0 0 C0 1 0 1 C1 1 0 C2s1 s0 Y 1
=NAND C0 C0 C1 C2 C3 C1
4 x 1
MUX Y C2 C3 s1 s0

7. Multiplexers 1 Can you implement a logic circuit withs1 s0 Y 1
=NOR C0 C0 C1 C2 C3 C1
4 x 1
MUX Y C2 C3 s1 s0
Can you implement a logic circuit with
THREE inputs using a 4 x 1 MUX?

8. 2 x 1 MUX is a universal element

9. Step 1 Implement the following logic equation using 2 x 1 MUXs
f = xy' + xz + y'z
x = 0
A = y'z
x = 1
B = y' + z + y'z

10. Step 2 A = y'z y = 0 0-input = z y = 1 1-input = 0 B = y' + z + y'z

11. 4 x 1 MUX
f = xy' + xz + y'z
The variable f is 1 if x > y or if x = y and z = 1.

12. Majority Circuit C0 C1
4 x 1
MUX Y C2 s0 C3 s0 s2 s1 1