Binary vs. BCD — conceptual distinction What is the correct statement that distinguishes pure binary coding from Binary-Coded Decimal (BCD)?

Introduction / Context:
Binary coding represents entire numbers directly in base 2, whereas BCD represents each decimal digit separately using a 4-bit code. This difference affects arithmetic efficiency, storage density, and ease of human-readable display.

Given Data / Assumptions:

• Binary uses powers of 2 for the whole number.
• BCD encodes digits 0–9 with 0000–1001.
• Higher 4-bit patterns (1010–1111) are not used for a single BCD digit.

Concept / Approach:
“Pure binary” means a number like 57 is stored as 111001 in base 2. In BCD, 57 is stored as two nibbles: 0101 (5) and 0111 (7). Thus binary coding is inherently base 2; BCD is a hybrid representation convenient for decimal I/O but less compact and slower for arithmetic without special hardware.

Step-by-Step Solution:

Verification / Alternative check:
Compare sizes: the number 99 is 1100011 in binary (7 bits) but 9 9 in BCD requires 8 bits (1001 1001), illustrating BCD’s overhead.

Why Other Options Are Wrong:

• BCD is pure binary: false, it encodes decimal digits in binary.
• Binary coding has a decimal format: false, it is base 2.
• BCD has no decimal format: false, it explicitly preserves decimal digits.

Common Pitfalls:
Assuming BCD arithmetic equals binary arithmetic performance; BCD often needs adjust/pack operations.

Final Answer:
Binary coding is pure binary.