Shannon*s Expansion Theorem

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) = a’b’c + ab
Multiplexer Universality for Logic Realization
Implementation directly from truth tables
f(a, b, c) = a’b’c + ab
for
for
for
for
(a,b)=(0,0)
(a,b)=(0,1)
(a,b)=(1,0)
( 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) = a’b’c + ab
for
for
a == 0
a == 1


f = b’ . c
f = ( b . c’ ) + ( b . c ) = b