Decoding a specific binary word — logic required for 1101 Which combination of gates can be used to decode and assert only when the 4-bit input equals 1101 (MSB→LSB)?

Introduction / Context:
Decoding a specific binary pattern means generating a HIGH output for exactly one input combination and LOW for all others. This is a standard application of AND gates together with necessary inversions to match required bit polarities.

Given Data / Assumptions:

• Target word: 1101 (bits b3 b2 b1 b0 = 1,1,0,1).
• Available primitives: AND, NAND, inverter, OR.
• Active-HIGH decode required.

Concept / Approach:
To assert for 1101, feed the AND gate with signals that are TRUE exactly for b3=1, b2=1, b1=0, b0=1. That requires using b3, b2, NOT(b1), and b0 as the AND inputs. Thus we need a single inverter to produce NOT(b1) and a 4-input AND to combine the four literals.

Step-by-Step Solution:

Verification / Alternative check:
Truth-table check: any deviation (e.g., b1=1) forces at least one AND input LOW, driving the output LOW, confirming exact decoding.

Why Other Options Are Wrong:

• 4-input AND alone: cannot handle the required inversion of b1.
• Adding an OR gate is unnecessary for a single minterm decode.
• NAND + inverter can realize the function but needs two inversions to get active-HIGH; with only one inverter stated, polarity would be wrong.

Common Pitfalls:
Mixing bit order (LSB/MSB) or forgetting to invert a bit that must be 0 in the target word.

Final Answer:
One 4-input AND gate, one inverter