Boolean Function with 8:1 Multiplexer

Boolean functions implementation with Multiplexer shown below with an example:

Let’s say having a boolean function given of four variables with its min-terms.

F(W, X, Y, Z) = Σ m(0, 1, 2, 3, 4, 8, 9, 12, 14, 15)

8:1 MUX(Multiplexer) is having 8 inputs and only one output. The output is F and Inputs are considering as W, X, Y, Z.

Considering 8 inputs from D0 to D7 as: D0, D1, D2, D3, D4, D5, D6, D7.

A table needs to be created to get exact input values for multiplexer according to given boolean function:

Table for getting Inputs of multiplexer with Min-terms in boolean function

On the table above, inputs are mentioned as values from 0 to 15 is inserted in sequence. Input of A is decided with certain rules which says:

1. Mark the numbers according to min-terms given in Boolean function.
2. Check the cases.
3. If Both numbers of W’ and W is marked then, input is 1.
4. If Both numbers of W’ and W is not marked, then input is 0.
5. If W’ number is marked and W is not marked then, input is W’.
6. If W number is marked and W’ is not marked then, input is W.

So, considering the above conditions and generating 8:1 Multiplexer:

8:1 Multiplexer for Boolean function

In the circuit of 8:1 MUX, Invertor (NOT) gate is used for W to W’ and X, Y, Z also act as inputs. Input 1 is coming from Vcc and 0 is from Ground. All the 8 inputs gave output as F.

This is how a boolean function is implemented with 8:1 Multiplexer.

A boolean function can be implemented with any other types of multiplexers say 2:1, 4:1, 16:1 ; depends on the number of variables.

I hope it helps :)

Thankyou