Hexadecimal to binary conversion: Convert the hexadecimal number 63₁₆ to its binary representation.

Introduction / Context:
Converting hexadecimal to binary is straightforward because each hex digit corresponds to exactly four binary bits. This mapping is used constantly when reading memory dumps, register values, and microcontroller configurations.

Given Data / Assumptions:

• Hex input: 63₁₆ (two hex digits).
• Target: binary representation.
• No need for leading zeros beyond those implied by each nibble.

Concept / Approach:
Translate each hex digit independently to a 4-bit pattern: 6 → 0110 and 3 → 0011. Concatenate the two nibbles to form the final binary number. Drop only superfluous leading zeros from the leftmost nibble if desired for compactness.

Step-by-Step Solution:
6₁₆ → 0110₂.3₁₆ → 0011₂.Concatenate: 0110 0011 → 1100011₂ (dropping the leading zero).

Verification / Alternative check:
Back-convert to hex: 1100011₂ grouped as 0110 0011 → 6 and 3 → 63₁₆. Decimal cross-check: 1100011₂ = 64 + 32 + 2 + 1 = 99; 63₁₆ = 6*16 + 3 = 99, confirming consistency.

Why Other Options Are Wrong:
1100111₂ corresponds to 67₁₆, not 63₁₆. 111011₂ corresponds to 3B₁₆ (with padding). Only 1100011₂ matches 63₁₆ precisely.

Common Pitfalls:
Misreading 3 as 0011 and then accidentally writing 0111; losing track of nibble boundaries; omitting necessary zero padding inside a nibble.

Final Answer:
1100011₂