Hex to Binary — Four Bits per Hex Digit Write the binary equivalent of the hexadecimal value F3A16 by expanding each hex digit into its 4-bit binary group.

Introduction / Context:
Mapping hexadecimal to binary is direct because a hex digit represents exactly four binary bits. This ability is essential for interpreting bit fields, control registers, and instruction encodings without intermediate decimal steps.

Given Data / Assumptions:

• Hex input: F3A16.
• Digit mapping: 0→0000, 1→0001, ..., 9→1001, A→1010, ..., F→1111.
• No sign, integer only.

Concept / Approach:
Translate each hex digit independently to a 4-bit binary group and concatenate in order. This preserves magnitude and avoids arithmetic errors that sometimes occur when converting via decimal.

Step-by-Step Solution:
1) Expand digits: F→1111, 3→0011, A→1010.2) Concatenate groups in the same order: 1111 0011 1010.3) Remove spaces for the final binary: 111100111010.4) Therefore, F3A16 corresponds to 111100111010 base 2.

Verification / Alternative check:
Convert back by grouping the binary in fours: 1111→F, 0011→3, 1010→A. This reconstructs F3A16 exactly.

Why Other Options Are Wrong:

• 111100111110: The last nibble 1110 represents E, not A.
• 000000111010 and 000011000100: These introduce leading zeros or different nibble values that do not match F3A16.

Common Pitfalls:
Reversing nibble order, dropping a nibble, or confusing A with 1011, which is actually B.

Final Answer:
111100111010