Multiplexers - ch. 6

ucla | CS M51A | 2023-01-24T14:34

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Table of Contents

• Definitions
• Big Ideas
  • 2-input Multiplexers (MUXes)
    • Shannon’s Decomposition (SD)
• Resources

Definitions

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Big Ideas

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2-input Multiplexers (MUXes)

• a 2-input multiplexer unit can be described by the switching expression

$z=MUX[x_1,x_0,s]=x_1\cdot s+x_0\overline{s}$

• the set of multiplexers $MUX$ is universal (can be represented as NOT and NAND)
• an example of implementations of NOT and AND:

$NOT(x)=MUX[0,1,x]=0\cdot x+1\cdot\bar x=\bar x\space$

Shannon’s Decomposition (SD)

$f(x_{n-1},…,x_0)=f(x_{n-1},…,1)\cdot x_0+f(x_{n-1},…,0)\cdot \bar x_0\implies$

• an example

  $z=x_3(x_2+x_0)x_1=MUX[x_3{x}_1,x_3{x}_2{x}_1,x_0]$

• you can use SD recursively to obtain a tree of multiplexers

Resources

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**SUMMARY
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