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)?
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AOne 4-input AND gate
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BOne 4-input AND gate, one OR gate
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COne 4-input NAND gate, one inverter
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DOne 4-input AND gate, one inverter
Answer
Correct Answer: One 4-input AND gate, one inverter
Explanation
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:
1) Identify required literals: b3, b2, b0, and b1' (inverted).2) Create b1' with one inverter.3) Feed b3, b2, b1', b0 into a 4-input AND.4) Output goes HIGH only when input equals 1101.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