Input width of a 1-of-16 decoder How many binary select inputs are required to address exactly one of sixteen outputs (a 1-of-16 decoder)?

Introduction / Context:
A 1-of-n decoder asserts exactly one output line out of n possibilities, based on a binary input code. The number of input bits needed equals log2(n). This relationship is central when selecting decoder sizes and building memory address decoders or chip-select trees.

Given Data / Assumptions:

• n = 16 desired outputs.
• Binary selection, one-hot output.
• No additional enable lines considered for the bit count.

Concept / Approach:

Compute k where 2^k = 16 → k = 4. Thus, four input bits uniquely select one of sixteen outputs.

Step-by-Step Solution:

Verification / Alternative check:

Check standard ICs like 74HC154 (4-to-16 line decoder): four select pins A,B,C,D with 16 outputs Y0..Y15.

Why Other Options Are Wrong:

2 bits → 4 outputs; 8 bits → 256 outputs; 16 bits → 65,536 outputs.

Common Pitfalls:

Counting enable pins as “inputs” for selection width; enable does not increase address space, it gates operation.

Final Answer:

4