Multiplexers and Demultiplexers
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
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 |
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 |