1-of-16 decoder input width: A “1-of-16” decoder asserts exactly one of sixteen outputs for each valid binary input code. How many input bits are needed so that all 16 outputs can be uniquely selected?

Introduction / Context:Decoders perform the inverse of encoders: they expand a compact binary code into a one-hot output. Determining the minimum number of input bits is fundamental to address decoding, chip selection, and memory banking.

Given Data / Assumptions:

• There are 16 mutually exclusive outputs.
• All outputs must be addressable by the input code.
• Inputs are binary and ideally minimal in number.

Concept / Approach:To uniquely select among 16 outputs, the decoder needs N bits where 2^N = 16. Since 2^4 = 16, the minimum is N = 4 input bits. With fewer than four bits, some outputs would be unreachable. With more than four bits, the mapping is not minimal (though sometimes used for hierarchical decoding).

Step-by-Step Solution:Check powers: 2^3 = 8 → insufficient.2^4 = 16 → exact match.Therefore, four input bits are required.This aligns with typical 4-to-16 decoder ICs.

Verification / Alternative check:Standard parts like the 74xx154 (4-to-16 line decoder) accept 4 inputs and provide 16 active-low outputs, confirming the calculation.

Why Other Options Are Wrong:Two and three bits cannot address 16 unique outputs. Six is excessive and non-minimal for selecting among sixteen lines.

Common Pitfalls:Confusing demultiplexers with decoders; forgetting enable pins that gate the outputs without changing the required input width.

Final Answer:four