Multiplexers and Demultiplexers

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The previous two sections were very exercise-heavy, so this section will be more exploratory. We will be exploring a few categories of circuits which are very commonly used in digital systems:

  • Multiplexers and Demultiplexers
  • Binary encoders and decoders (note that these are distinct from the binary to 7-segment decoders we have previously used)

Multiplexers and Demultiplexers

An n-bit multiplexer has the following function:

Given 2n 1-bit inputs and one n-bit input, give one 1-bit output. If the n-bit input is x, then the output is equal to the xth 1-bit input.

More simply, a multiplexer takes several inputs and a number, and forwards the input at that position to the output.

Let us recall the multiplexer from earlier

o = s'x + sy

This is its truth table:

s a b o
L L L L
L L H L
L H L H
L H H H
H L L L
H L H H
H H L L
H H H H

This can be simplified to:

s a b o
L X X a
H X X b

Upload a truth table and a circuit diagram for a 2-bit multiplexer, i.e. a circuit which selects between 4 inputs.
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A demultiplexer does the exact opposite. Given one n-bit input and one 1-bit input, gives 2n 1-bit outputs. If the n-bit input is x, then the xth 1-bit output is equal to the 1-bit input, and all the other outputs are LOW

Hence, we can construct the following truth table for a 1-bit demultiplexer:

s i a b
L X i L
H X L i

Upload a truth table and a circuit diagram for a 2-bit demultiplexer, i.e. a circuit which selects between 4 outputs to send the input to.
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