Why hexadecimal is popular — primary advantage: Judge the statement: “The primary advantage of the hexadecimal numbering system is the ease of conversion to and from binary.”

Introduction / Context:Choosing a base representation in engineering is about readability and efficiency. Hexadecimal is ubiquitous in debugging, addressing, and embedded development because it compresses binary into a compact, human-friendly form while preserving an exact, simple mapping.

Given Data / Assumptions:

• 1 hex digit corresponds exactly to 4 binary bits (one nibble).
• No arithmetic complexity is introduced by this mapping.
• We compare to other bases such as decimal and octal.

Concept / Approach:The neat 4-bit grouping means any binary pattern can be rewritten by grouping bits into nibbles and translating each nibble directly into one hex digit. This direct mapping is the core advantage: conversion is trivial and lossless. Decimal lacks a simple fixed-size mapping to binary; octal uses 3-bit groupings but is less aligned with byte boundaries than hex.

Step-by-Step Solution:Group a binary stream into 4-bit nibbles.Translate each nibble to one hex symbol (0–9, A–F).Reverse mapping is equally simple: expand each hex digit back to 4 bits.Conclude: ease of conversion is the principal practical benefit.

Verification / Alternative check:Memory dumps, register maps, and instruction encodings are routinely presented in hex for this reason; tools like debuggers show values in hex to mirror binary structure.

Why Other Options Are Wrong:Hex does not “save memory” relative to binary; it is just a notation. Limitations to signed integers are irrelevant—mapping works for any bit pattern.

Common Pitfalls:Forgetting to pad leading zeros to complete nibbles; mixing endianness concerns (byte order) with base representation.

Final Answer:Correct