# Boolean Algebra for 1.9 Demulitplexor

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 Administrator The expanded truth table for mux will have inputs sel and in and outputs a and b: ```sel|in || a | b ---|---||---|--- 0 | 0 || 0 | 0 0 | 1 || 1 | 0 1 | 0 || 0 | 0 1 | 1 || 0 | 1 ```Since there are two outputs, you need two Karnaugh maps, one for each output. Since there are only two variables, they are going to be 2 by 2 k-maps, which are not too interesting. When you have more than 2 inputs, then things become more interesting. For the optimum solution you need to start by looking for minterms that are common to both k-maps. Say we have a part with three inputs a, b, and c, and two outputs F and G whose k-maps are: ``` | bc | bc F | 00 01 11 10 G | 00 01 11 10 ---+---+---+---+---+ ---+---+---+---+---+ 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | a +---+---+---+---+ a +---+---+---+---+ 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | +---+---+---+---+ +---+---+---+---+ ```F and G have the minterm (~b)c in common so that Not and And gate can be shared with the circuits for both outputs.       F = ab + (~b)c       G = (~a)(~c) + (~b)c This can get complex rather quickly.  Especially when you add "don't care" values to the functions. --Mark