Multiplexers

Selects 1 output from a bunch of inputs. MUX’s These guys are everywhere.

• The “selector” S has $ciel(lo{g}_2(N))$ data bits where $N$ is the number of inputs to the mux
  • S selects between the different inputs you pass and “passes through” the selected.
  • e.g. 7 inputs means your S would need to be $3$ data bits as that represents at most 8 numbers = 8 inputs!
• M represents the output depending on what input the $S$ chooses M to “pass through”
• The inputs themselves can have $n$ data bits (the output should have the same # of data bits too)

The "/" with the n above specifies how many bits the "streams" are passing. Refer to Data Bits

An 8-to-1 mux has 8 inputs, 1 output, and should have 3 select bits.

Design

• You don’t really need a k-map since $M=Y\cdot S+X\cdot \bar{S}$ makes sense intuitively!
  • If S is true, return Y. If S is false, return X. Nothing fancy here :)
• Similar thing for a 4-to-1 mux, for instance: $M={\bar{S}}_0\cdot {\bar{S}}_1\cdot X+{\bar{S}}_1\cdot S_0\cdot Y+\dots$
• For each permutation of $S_0,S_1,{\bar{S}}_0,{\bar{S}}_1$, you would have one unique output!

Use case

• Think of TVs
  • there is a mux to determine your channel.
• Think of surveillance cameras
  • You can only display 1 of them at a time by selecting. Think fnaf lol