Question

The propagation delays of the XOR gate, AND gate, and multiplexer (MUX) in the circuit shown in the figure are 4 ns, 2 ns, and 1 ns, respectively. 

If all the inputs \( P \), \( Q \), \( R \), \( S \), and \( T \) are applied simultaneously and held constant, the maximum propagation delay of the circuit is

• A. 3 ns
• B. 5 ns
• C. 6 ns
• D. 7 ns

Hint:

When calculating the maximum propagation delay in a combinational circuit, sum the delays along the longest path from the inputs to the output.

Answer 1

The Correct Option is C

In the given circuit, the delay is determined by the longest path from the inputs to the output. We need to calculate the total propagation delay for each possible path and determine the maximum delay. 1. Path 1: P and Q through the XOR gate - Delay of the XOR gate = 4 ns. 2. Path 2: R and S through the AND gate - Delay of the AND gate = 2 ns. 3. Path 3: Inputs to the MUX - Delay of the MUX = 1 ns. - The delay for this path involves the time taken by the XOR gate, the AND gate, and the multiplexer. The total delay along the longest path is: \[ \text{Total delay} = \text{XOR delay} + \text{AND gate delay} + \text{MUX delay} = 4 \, \text{ns} + 2 \, \text{ns} + 1 \, \text{ns} = 6 \, \text{ns}. \] Thus, the maximum propagation delay of the circuit is 6 ns. Final Answer: 6 ns