Why Do We Use Multiplexers in Digital Systems?

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RMZ
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I don't understand what the point of a multiplexer is. I see the purpose of a selector circuit and a decoder, as an appropriate address will cause a unique gate to output a logic high, but I don't see the point of "OR"ing them together to get a single one or zero at the end. Please help
 
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A mux simply allows you to do a controlled select of one of several signals.

Suppose for example that you have a recording device but only one path to it (very common in, for example, tape or disk data recording). A mux allows you to record each of numerous signals, sampled one at a time, and then repeat that sequence over and over. Thus you will hear the phrase "time division multiplexor".
 
So does that mean that in:
(D1 and D2 mean AND gate1 and 2, while d1 and d2 mean AND gate 1 and 2 in the decoder.)
A--------D1---OR
B--------D2---the same OR
d1-----D1
d2-----D2

if I input an address that will "enable" D2 to change the OR gate's output, as I pulse a logic high/low through B the MUX will mimic the output of D2?
 
I have no idea what you are talking about. Draw a box with 4 inputs and one output. Label the inputs A, B, C, D and label the output A OR B OR C OR D (but NOT logically ORed together, just selected as one of the four)

Of course, you also have to have 2 control line inputs to tell the mux which of the 4 inputs to pick for the output.