# Shannon's Expansion Theorem - CS Department Multiplexers Functional Description and Symbols

Where, N = {1, 2, 3, .. , }

Where, N = {1, 2, 3, .. , }

Where, N = {1, 2, 3, .. , }

Where, n = 2(m+1) 1

m = {0,1, 2, 3, .. , } Operation of a 2-to-1 line Mux

Operation of a 2-to-1 line Mux

Operation of a 2-to-1 line Mux Operation of a 4-to-1 line Mux

Operation of a 4-to-1 line Mux

Operation of a 4-to-1 line Mux Operation of a 4-to-1 line Mux

Operation of a 4-to-1 line Mux

Operation of a Multiplexer Tree Operation of a Multiplexer Tree

Operation of a Multiplexer Tree

Operation of a Multiplexer Tree Operation of a Multiplexer Tree

Implementing Functions Using Multiplexers

Multiplexer Universality for Logic Realization Implementation directly from truth tables

f(a, b, c) = abc + ab Multiplexer Universality for Logic Realization

Implementation directly from truth tables f(a, b, c) = abc + ab for ( a , b ) = ( 0 , 0 ) for ( a , b ) = ( 0 , 1 )

for ( a , b ) = ( 1 , 0 ) for ( a , b ) = ( 1, 1 )

f=c f=0 f=0

f=1 Multiplexer Universality for Logic Realization

Implementation directly from truth tables f(a, b, c) = abc + ab

for a == 0 for a == 1

f = b . c f = ( b . c ) + ( b . c ) = b