Binary to hexadecimal conversion: Convert the binary number 1101100111111000₂ to hexadecimal.

Introduction / Context:
Because 16 = 2^4, converting from binary to hexadecimal is performed by grouping binary digits in sets of four (nibbles). Each group maps directly to a single hex digit. This is essential in digital design, firmware work, and reading machine code dumps.

Given Data / Assumptions:

• Binary input: 1101100111111000₂.
• Output: hexadecimal representation.
• No leading zeros required because the bit-length is already a multiple of 4 (16 bits).

Concept / Approach:
Split the 16-bit string into 4-bit groups from left to right, translate each 4-bit group to its hex digit using the mapping 0000→0 to 1111→F, then concatenate the digits in order.

Step-by-Step Solution:
Group: 1101 1001 1111 1000.Map: 1101→D, 1001→9, 1111→F, 1000→8.Combine: D 9 F 8 → D9F8₁₆.

Verification / Alternative check:
Decimal spot-check of the first nibble: 1101₂ = 13 → D; last nibble: 1000₂ = 8 → 8. Intermediate nibbles match 9 and F, confirming D9F8₁₆ is consistent throughout.

Why Other Options Are Wrong:
D8F8₁₆ incorrectly maps the second nibble; A8B9₁₆ and 7891₁₆ are unrelated conversions. Only D9F8₁₆ matches the nibble mapping of the given binary.

Common Pitfalls:
Grouping bits from the right and misaligning nibbles; forgetting to preserve the original bit order when translating; misreading 1111 as E (14) instead of F (15).

Final Answer:
D9F8₁₆