Hex to binary — four-digit example Convert the hexadecimal number 8B3F₁₆ into its binary equivalent.

Introduction / Context:Because each hex digit represents exactly four binary bits, converting multi-digit hexadecimal to binary is fast and lossless. This is a routine operation when reading register dumps, addresses, or configuration values in embedded systems and digital electronics.

Given Data / Assumptions:

• Hex input: 8 B 3 F.
• Nibble mappings: 8 → 1000, B → 1011, 3 → 0011, F → 1111.
• Order of digits is preserved.

Concept / Approach:Translate each hex digit independently to a 4-bit group and then concatenate in the same left-to-right order. No arithmetic is needed beyond table mapping 0–F → 0000–1111.

Step-by-Step Solution:

Verification / Alternative check:Group the binary back into nibbles: 1000 1011 0011 1111 → 8 B 3 F → 8B3F₁₆, confirming accuracy.

Why Other Options Are Wrong:

• 1011001111100011: nibbles are out of order (wrong concatenation).
• 011010: far too few bits.
• 35647: decimal digits, not binary.

Common Pitfalls:Reversing nibble order or failing to keep four bits per hex digit (especially losing leading zeros within a nibble).

Final Answer:1000101100111111