Obtain the Boolean expression of the 2:1 MUX shown in the figure below. ?

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Answer

Boolean Expression of 2:1 MUX

A 2:1 MUX is a combinational logic circuit that selects one of two inputs based on the value of the select input. The circuit diagram of a 2:1 MUX is shown below:

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Truth Table

The first step in obtaining the Boolean expression of the 2:1 MUX is to create a truth table. The truth table shows the output of the circuit for all possible combinations of inputs and select:

Select	Input A	Input B	Output
0	0	X	0
0	1	X	1
1	X	0	0
1	X	1	1

Where X is a don't care value.

Boolean Expression

Using the truth table, we can create the Boolean expression for the output:

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The Boolean expression for the output of the 2:1 MUX is:

Output = (Select * Input B) + ((NOT Select) * Input A)

This expression can be simplified using Boolean algebra and the laws of logic.

Explanation

The 2:1 MUX selects one of two inputs based on the value of the select input. If select is 0, the output is equal to input A. If select is 1, the output is equal to input B. The Boolean expression reflects this behavior by using the select input to determine which input to pass through to the output.

The first term (Select * Input B) represents the case where select is 1 and input B is passed through to the output. The second term ((NOT Select) * Input A) represents the case where select is 0 and input A is passed through to the output. The NOT operator is used to invert the value of select.

By combining these two terms with the OR operator, we

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