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Computer organization Notes--Multiplexer

Multiplexer is a special type of combinational circuit. It is a digital circuit which converts many of input information signals into one output. It is also called as data selector because a multiplexer (MUX) is a digital switch which connects data from one of n sources to the output. A number of select inputs determine which data source is connected to the output. Generally for 2n input lines, n selection lines are required. The bit combination of selection lines determine which input data is selected for output and alternative name for multiplexer is “MUX”. There are n-data inputs, one output and m select inputs with 2m = n. It is a digital circuit which selects one of the n data inputs and routes it to the output. The selection of one of the n inputs is done by the selected inputs. Depending on the digital code applied at the selected inputs, one out of n data sources is selected and transmitted to the single output Y. E is called the strobe or enable input which is useful for the cascading. It is generally an active low terminal that means it will perform the required operation when it is low. As in decoders, multiplexers may have an enable input to control the operation of the unit. When the enable input is in the inactive state, the outputs are disabled, and when it is in the active state, the circuit functions as a normal multiplexer.
The block diagram of an n-input and m Control signal Multiplexer can be drawn as follows:

Here m is less than or equal to 2n.
Multiplexers can also be used as programmable logic devices, specifically to implement Boolean functions. Any Boolean function of n variables and one result can be implemented with a multiplexer with n selector inputs. These multiplexers are used in building digital semiconductors like CPU and graphics controllers. They are also used in communication like telephone network.
Applications of MUX
1. MUXs are used to reduce the number of interconnections.
2. MUXs are used for designing common bus.
3. MUXs can be used to realize Boolean expression as well as to realize combinational circuits.
Let us consider the case of 4 x 1 Line Multiplexer. Where each of the four inputs are applied to one of the inputs of AND gate. The 2 selection inputs S0 and S1 are decoded to select a particular AND gate and output of the AND gates are applied to single OR gate.
The function table/characteristic table and block diagram for a 4 x 1 multiplexer can be written as

Note that if both the selection lines S0 and S1 are 00, then data on input line I0 will appear on the output. Thus, data output Y is equal to I0 if and only if S1 = 0 and S0 = 0. Therefore, we can write output function Y as Y = I0S1’S0’
Similarly, the data output is equal to I1, I2, and I3 for Y = I1S1’S0, Y = I2S1S0’ and Y = I3S1S0 respectively. Therefore, total multiplexer logic expression, formed from ORing terms is
Y = I0S1’S0’ + I1S1’S0 + I2S1S0’ + I3S1S0
The logic diagram of a 4 x 1 multiplexer can be drawn as follows.

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