For a 2-to-1 Multiplexer with inputs I0 = 0, I1 = 1, and select line S = 1, what is the value of the output Y?

Explanation:

A 2-to-1 multiplexer is a combinational logic circuit that selects one of the two input signals (I₀ or I₁) and forwards it to a single output (Y), based on the value of the select line (S). The operation of the multiplexer is controlled by the binary value of the select line. A multiplexer is often referred to as a "data selector" because it selects one input to pass to the output.

Working Principle: The 2-to-1 multiplexer works as follows:

• When the select line (S) is 0, the output (Y) is equal to the input I₀.
• When the select line (S) is 1, the output (Y) is equal to the input I₁.

The logical expression for the output (Y) of a 2-to-1 multiplexer can be written as:

Y = (S' × I₀) + (S × I₁)

Here:

• S' is the complement of the select line S.
• × represents the logical AND operation.
• + represents the logical OR operation.

Correct Option Analysis:

Let us solve the problem step-by-step to determine the correct output for the given inputs:

Given:

• Input I₀ = 0
• Input I₁ = 1
• Select line S = 1

Using the logical expression for the output of a 2-to-1 multiplexer:

Y = (S' × I₀) + (S × I₁)

Step 1: Find the complement of S (S'):

Since S = 1, the complement of S (S') is:

S' = 0

Step 2: Calculate the first term (S' × I₀):

Substitute S' = 0 and I₀ = 0 into the expression:

S' × I₀ = 0 × 0 = 0

Step 3: Calculate the second term (S × I₁):

Substitute S = 1 and I₁ = 1 into the expression:

S × I₁ = 1 × 1 = 1

Step 4: Add the two terms to find the output Y:

Y = (S' × I₀) + (S × I₁)

Substitute the values:

Y = 0 + 1 = 1

Therefore, the output of the 2-to-1 multiplexer is:

Y = 1

Correct Option:

The correct option is Option 3: 1