Multiplexer

A multiplexer is a combinational circuit that selects binary information from one of many input lines and directs it to a single output line. It is also called as a data selector since it selects one of many inputs at a time and directs it to the output. The selection of a particular input line is controlled by a set of
selection lines.

Normally, there are 2n input lines and n selection lines whose bit combinations determine which input is selected.

4 to 1 line multiplexer

4x1 Multiplexer has four data inputs I3, I2, I1 & I0, two selection lines s1 & s0, and one output Y.

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 Fig: Block diagram of 4 to 1 line multiplexer

One of these 4 inputs will be connected to the output based on the combination of inputs present at these two selection lines.

Truth table

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From Truth table, we can directly write the Boolean function for output, Y as

Y=S1′S0′I0+S1′S0I1+S1S0′I2+S1S0I3

Logic Diagram

We can implement this Boolean function using Inverters, AND gates & OR gate.

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To demonstrate the above circuit,

•  Consider the case when s1s2= 10.
• The AND gate associated with input I2 has two of its inputs equal to 1 and the third input connected to I2.
• The other three AND gates have at least one input equal to 0, which makes their outputs equal to 0.
• The OR gate output is now equal to the value of I2, thus providing a path from the selected input to the output.

Q. Show how 4-to-1 multiplexer can be obtained using 2-to-1.
Solution:
Logic equation for 2-to-1 MUX Y= s'I0 + sI1
The logic equation for 4-to-1 MUX Y=S1′S0′I0+S1′S0I1+S1S0′I2+S1S0I3

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8 to 1 line Multiplexer

For the combination of a selection input, the data line is connected to the output line. The 8-to-1 multiplexer requires 8 AND gates, one OR gate, and 3 selection lines. As an input, the combination of selection inputs is giving to the AND gate with the corresponding input data lines.

In a similar fashion, all the AND gates are given connection. In this 8*1 multiplexer, for any selection line input, one AND gate gives a value of 1. The remaining all AND gates give 0. And, finally, by using OR gate, all the AND gates are added; and, this will be equal to the selected value.

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