Chapter 6 Notes
6.4 Networks with Two Input Multiplexers
Two Input Multiplexer - A mux selects output from two or
more inputs. It acts as a selection switch, much as the TV channel changer
can select from several channels as input to output to the single screen.
The switching function table for a two input multiplexer that uses a selector
select between two inputs, x1 and x0 is:
s x1 x0 | z s | z x1x0
0 0 0 | 0 0 | x0 s \00 01 11 10
0 0 1 | 1 1 | x1 0| 0| 1| 1| 0|
0 1 0 | 0 1| 0| 0| 1| 1|
0 1 1 | 1
1 0 0 | 0 z = x1s + x0s'
1 0 1 | 0
1 1 0 | 1
1 1 1 | 1
The gate network to implement a two input mux and symbol is:
Universal Set - Multiplexers constitute a universal set and are
sometimes used, as in some FPGA's, as the basis of all logic operations.
The following implement the NOT, AND, OR operations using a two input Multiplexer.
z = 0x1+ 1x1' = x1'
z = x1x0+ 0x0' = x1x0
z = 1x0+ x1x0' = x1+x0
Programmable - The multiplexer is in a sense programmable since
other logic operations can be produced by choosing different inputs. Consider
the useful expression x2x0+x3x0'
Shannon's Decomposition - f(xn-1,xn-1,...,x0)
= f(xn-1,xn-1,...,1) x0+ f(xn-1,xn-1,...,0)x0'
From the text example,
z = x3(x1+x2x0) = x3x1+x3x2x0
f(x3,x2,x1,0) = x3x1x0'+x3x20
= x3x11 + 0 = x3x1x0'
f(x3,x2,x1,1) = x3x1x0+x3x2x0
= x3x11+x3x21 =
z = x3x1x0' + x3x1x0+
x3x2x0 = x3x1x0'
This was implemented by:
Building Blocks for Digital Design - Larger multiplexers can
be constructed from smaller ones by casading. In the following figure,
two input multiplexers are used to construct a four input multiplexer.
The two selectors, s1s0, when 2 (s1=1
and s0=0) selects x2 or the 102 position.
The algebraic expression for a four-input multiplexer is: z = x3s1s0+
which would have 6 inputs and 64 rows for a truth table solution. The functional
behavior for the 4-input multiplexer and modular implementation would be:
|s1 s0 | Output
0 0 | x0
0 1 | x1
1 0 | x2
1 1 | x3