Hex to binary — two-digit example Convert the hexadecimal value C1₁₆ to an 8-bit binary representation.

Introduction / Context:Hexadecimal maps cleanly to binary because each hex digit corresponds to 4 bits (a nibble). Converting hex to binary is a matter of replacing each hex digit with its 4-bit equivalent and concatenating the results.

Given Data / Assumptions:

• Hex input: C1.
• Hex-to-binary nibble mapping is used.
• We want a compact 8-bit result.

Concept / Approach:Map C → 1100 and 1 → 0001, then join the two nibbles in the same order. No arithmetic is required beyond table lookup for the digits 0–F.

Step-by-Step Solution:

Verification / Alternative check:Convert back via grouping: 1100 0001 → C1 in hex, confirming correctness.

Why Other Options Are Wrong:

• 1000111, 111000100, 111000001: wrong bit lengths or wrong nibble mappings; do not decode back to C1.

Common Pitfalls:Dropping leading zeros in the lower nibble or reversing nibble order.

Final Answer:11000001