Multiplexer as a Universal Function Generator

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Presentation transcript:

Multiplexer as a Universal Function Generator Discussion D4.3

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

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

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

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

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

Multiplexers 1 Can you implement a logic circuit with s1 s0 Y 1 =NOR C0 0 0 C0 0 1 C1 1 0 C2 1 1 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?

2 x 1 MUX is a universal element

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

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

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

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