# Multiplexers Oh My!

I’ve been playing more with Logisim – getting used to the UI and building more circuits – multiplexers and demultiplexers in fact.

So last time I showed you the MUX 2×1 I built to help create a single “bit” of memory:

To recap, a multiplexer lets you choose between two (or more) input lines (e.g. A0 and A1 above), sending only one of them to the output (X). The SEL line states which of the two inputs (SEL = 0 for A0, SEL = 1 for A1) to pass through to X.

That’s great for two lines, but what if you have more to chose from? Turns out this basic logic can be relatively easily extended to additional lines by combining multiple MUXs. Let’s start with a MUX4x1:

So now we have two SEL lines (SEL0 and SEL1) and four input lines to choose from (A0 to A3). How do we set the SEL lines to pick a particular input line?

If you’re not already familiar with binary numbers, now would be a good time to read up ðŸ™‚

Given two SEL lines (each being 0 or 1) we can create 2^2 = 4 values in binary: 00, 01, 10, 11 which correspond to the decimal values 0, 1, 2 and 3. Hmm, notice that we named the input lines above A0, A1, A2 and A3? That wasn’t coincidental ðŸ™‚

That means in order to pick input A2 as our output (as in the diagram above) we need to set the two SEL lines to the binary number 10 (or 2 in decimal) or in other words SEL0 = 0 and SEL1 = 1.

Why that and not SEL0=1 and SEL=0?

In terms of binary number counting SEL0 represents the “least significant digit” (right most) of the two digit binary number (e.g. 0 of 10); which means that it repeats each time a more significant digit (e.g. SEL1) changes. In decimal numbers we might count from 0 to 9, 10 to 19, 20 to 29, etc. Binary works the same way, but we only have 1 and 0 to work with. So 00, 01, 10, 11.

Read that over a couple times if you need to ðŸ™‚

Okay, so with SEL0 representing the least significant digit, let’s see what the circuit does with it. You can see that SEL0 (0) is fed into the two both of the MUX2x1’s on the left. This means that the top MUX2x1 will select A0 (the first of its two inputs) and the bottom MUX2x1 will select A2 (the first of its two inputs).

That narrows down our options from 4 lines to just 2 (A0 or A2). Now we need to choose which of those two to output – that’s where the “most significant digit” (SEL1) comes into play. The outputs of the two MUX2x1’s are fed into a third MUX2x1 with the SEL1 line making the choice. In this case, SEL1=1 so its second input (A2, the output from the lower MUX2x1) is output on X.

Yup, yup.

Following through with this logic we get…drum roll…a MUX8x1 and MUX16x1!

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Cool huh? Maybe a little hypnotic too ðŸ™‚

That’s all for now, I’ll write about the demultiplexers next time!