BCD vs hexadecimal — Evaluate: “Hexadecimal is used to encode BCD numbers.” Clarify the distinction between 4-bit hex digits and BCD nibbles.

Introduction / Context:
Hexadecimal (base 16) and Binary-Coded Decimal (BCD) both use 4-bit groups, which often leads to confusion. However, they encode different domains: hex digits represent values 0–15, while standard BCD encodes decimal digits 0–9 only. This question probes whether you can separate these encodings conceptually and practically.

Given Data / Assumptions:

• Hex digits: 0–9, A–F mapping to 0–15.
• BCD digits: 0000–1001 valid; 1010–1111 are invalid in standard BCD.
• Use cases: hex for compact representation of arbitrary bit patterns; BCD for decimal-exact quantities.

Concept / Approach:
Although both use nibbles, BCD is not “encoded by hex.” BCD stores each decimal digit separately in 4 bits to preserve decimal semantics (e.g., 39 decimal → BCD 0011 1001). Hexadecimal is a base-16 numeral system; 0x27 equals decimal 39 but as a single base-16 number, not two decimal digits encoded. Treating hex and BCD as interchangeable causes value misinterpretations in registers and memory maps.

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