Question

In the given network of AND and OR gates, output Q can be written as (assuming n even):

• A. \(X_0X_1 + X_2X_3 + ... + X_n\)
• B. \(X_0X_1 + X_1X_2 + X_3X_2 ... X_n + X\)
• C. \(X_0X_1...X_{n-1} + X_2X_3X_5...X_{n-1} + X_{n-2}X_{n-1} + X_n\)
• D. \(X_0X_1...X_{n-1} + X_2X_3X_5...X_{n-1} + X_{n-2}X_{n-1} + X_n\)

Hint:

Simplify Boolean expressions by using the properties of AND and OR gates, and check for patterns in how the inputs are combined.

Answer 1

The Correct Option is D

1. Step 1: The Boolean expression for a series of AND and OR gates can be simplified using Boolean algebra.
2. Step 2: In the given configuration of AND and OR gates, the output \( Q \) can be simplified by examining how each input is combined through AND and OR operations. Since \( n \) is even, the output can be expressed as the sum of products of adjacent inputs.
3. Step 3: The correct Boolean expression is: \( Q = X_0X_1 + X_2X_3 + \dots + X_n \), as each AND gate operates on pairs of adjacent inputs.