Chapter 6 Notes (original) (raw)
- 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_s_to 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.
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'implemented by:
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 = x3x1x0+ x3x2x0
so z = x3x1x0' + x3x1x0+ x3x2x0 = x3x1x0' + x3(x1+x2)x0
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+ x2s1s0'+x1s1's0+x0s1's0' 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 |  |
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