Decoder size from truth-table labeling A truth table whose output columns are labeled 0 through 15 most likely corresponds to which decoder integrated circuit (IC) type?

Introduction / Context:
Decoders assert exactly one of many outputs based on a binary input code. When a truth table shows output lines numbered 0–15, it strongly suggests a 1-of-16 decode, commonly described as a “hexadecimal” (base-16) decoder because there are 16 distinct outputs for the 16 possible 4-bit input combinations.

Given Data / Assumptions:

• Outputs explicitly labeled 0,1,2,…,15.
• Binary input width implied: 4 bits (2^4 = 16).
• Standard active-high decoding assumed (one-hot output).

Concept / Approach:

A 1-of-n decoder maps an n-ary selection from log2(n) binary inputs to n outputs. For 16 outputs, log2(16) = 4 inputs. Therefore a 1-of-16 decoder (often called hexadecimal) fits the 0–15 labeling perfectly.

Step-by-Step Solution:

Verification / Alternative check:

Typical parts (e.g., 74HC154) implement 4-to-16 decoding with outputs Y0..Y15, aligning with the 0–15 truth-table columns.

Why Other Options Are Wrong:

Dual octal outputs: would indicate two separate 1-of-8 sections, not a single 0–15 set.

Binary-to-hexadecimal: a converter/encoder term, not a one-hot decoder.

Hexadecimal-to-binary: describes an encoder, not a decoder with 16 distinct output lines.

Common Pitfalls:

Confusing decoders (one-hot outputs) with encoders/code converters (multi-bit outputs). Labeling 0–15 almost always implies 4-to-16 decoding.

Final Answer:

hexadecimal 1-of-16