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I have a circuit where i have 4 binary numbers, they are all stored in D FlipFlops. I want to be able to pull out one of those numbers based on an "index" number. The index number would be a 2 bit binary number that would be created by pushing 2 buttons. So lets say my numbers are A, B, C and D. When the index number is 00(0) i would like to have A as an output, when the index number is 01(1) i would like B to be the output, when the index number is 10(2) i would like C to be the output and when 11(3) is the number i would like D to be the output. So my question is: do i use a multiplexer or a demultiplexer to do this? Can you recommend me a chip out of the 74LS series that would be able to do this? All relevant answers are welcome.

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You need a multiplexer, since you go from a number of inputs to a single output. The 74HC153/253 is a dual 4-to-1 multiplexer. For other input configurations see this overview.

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One could use a multiplexer as described, or if you have no need to do anything with more than one of the numbers at a time, you could store them in flops that have a Tri-State® brand output or equivalent, tie all of the outputs together, and then use a demultiplexer to enable one of the outputs. This latter approach could save a fair bit of circuitry if the numbers are many bits "wide". For example, one could four eight-bit numbers using four 74HC574 chips, and then use a single 74HC138 to enable one of the outputs (the 74HC138 could be used to select among eight such chips), for a total of five chips total. Otherwise if the numbers are eight bits wide one would probably have to use four of the two-bit multiplexer chips described by stevenvh. If you need to have the the latch outputs available "directly" in addition to multiplexed, putting all the devices on a bus may make the wiring easier than having separate connections from each latch bit to a different multiplexer input.

If you have four 8-bit numbers, and don't need separate register outputs, you can get by with 5 chips. If you do need separate latch outputs, you could add four 74HC541 or 74HC573 chips for that purpose for nine total, or you could use four 8-bit registers and four 74HC153/253's.

If you have four 4-bit numbers, you could use the latches and need separate register outputs, add either a 74HC138 (as above) and two 74HC541's or else use two 74HC153/253 (the latter would probably be a better choice).

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