BCD vs. pure binary — “A Binary-Coded Decimal (BCD) representation of a given numeric value always requires more bits than its pure binary representation.” Evaluate.

Introduction / Context:
Binary-Coded Decimal encodes each decimal digit with a fixed 4-bit nibble (0000–1001 valid). Pure binary uses the minimum number of bits needed to represent the numeric value by powers of two. This question contrasts representation efficiency for the same value across these two encodings.

Given Data / Assumptions:

• BCD: 4 bits per decimal digit; 10–15 patterns are unused in standard BCD.
• Binary: minimum-length base-2 positional representation.
• We compare equal numeric values, not different numbers.

Concept / Approach:
Because BCD allocates four bits per decimal digit regardless of magnitude, it is wasteful compared to binary. For example, the decimal value 99 needs two BCD nibbles (8 bits) but only 7 bits in pure binary (1100011). This overhead persists and grows with larger magnitudes, so BCD invariably uses at least as many—and typically more—bits.

Step-by-Step Solution:

Verification / Alternative check:

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