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I understand the concept of a multiplexer and I can understand how n-1 multiplexers function. Your just sending a select signal to tell the multiplexer which of the inputs at the input pins to let through on the other side.

But what does an 8-4 multiplexer work? I'm specifically talking about the 74LS257. I tried looking at the datasheets, but I still don't get it.

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Another way of stating a 8-4 multiplexor is as four copies of a 2-1 multiplexor. The SELECT pin connects to all multiplexors, so they all choose the '0' or '1' input together. This allows you to switch 4-bit buses relatively easily with few pins.

Annotated Datasheet Image

The datasheet is a little more confusing because it includes the discrete logic version of a multiplexor. They probably did that so that the tri-state output can be shown un-ambiguously.

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It's four copies of 2:1 multiplexers. A single select controls all four of them.

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