Hexadecimal to binary — nibble-by-nibble conversion Convert the hexadecimal number 14B16 to its binary (base-2) representation.

Introduction / Context:Each hexadecimal digit corresponds exactly to a 4-bit binary nibble. Therefore, converting hex to binary is as simple as translating each hex digit to 4 bits and concatenating the results. This method is reliable and fast for hand calculations and code alike.

Given Data / Assumptions:

• Hex input: 14B16 (digits 1, 4, B).
• We must output an equivalent binary string; options append a trailing 2 to denote base-2.
• Leading zeros are acceptable to keep full nibbles.

Concept / Approach:

Use the nibble map: 1→0001, 4→0100, B→1011. Concatenate in the same order to produce a 12-bit result, preserving leading zeros for the most significant nibble if needed.

Step-by-Step Solution:

Verification / Alternative check:

Convert back: split 000101001011 into nibbles 0001(1), 0100(4), 1011(B) → 14B16; the round-trip matches.

Why Other Options Are Wrong:

1011010000012 and 1101010000012 reorder bits, not a valid per-nibble translation of 1, 4, B.

0001010011012 flips two bits in the final nibble (1011 → 1101), corresponding to D rather than B.

Common Pitfalls:

Dropping leading zeros in the most significant nibble, writing nibbles in reverse order, or confusing B(1011) with D(1101). Always check each nibble against the standard hex–binary table.

Final Answer:

0001010010112