Question:
In the given network of AND and OR gates, output Q can be written as (assuming n even):
In the given network of AND and OR gates, output Q can be written as (assuming n even):
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Simplify Boolean expressions by using the properties of AND and OR gates, and check for patterns in how the inputs are combined.
Updated On: Apr 16, 2025
- \(X_0X_1 + X_2X_3 + ... + X_n\)
- \(X_0X_1 + X_1X_2 + X_3X_2 ... X_n + X\)
- \(X_0X_1...X_{n-1} + X_2X_3X_5...X_{n-1} + X_{n-2}X_{n-1} + X_n\)
- \(X_0X_1...X_{n-1} + X_2X_3X_5...X_{n-1} + X_{n-2}X_{n-1} + X_n\)
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The Correct Option is D
Solution and Explanation
- Step 1: The Boolean expression for a series of AND and OR gates can be simplified using Boolean algebra.
- 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.
- 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.
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