Hex arithmetic practice Compute ACE₁₆ − 999₁₆ and report the result in hexadecimal.

Introduction / Context:
Hexadecimal subtraction is routine in digital design for addresses and register values. This exercise reinforces place-value borrowing in base-16 arithmetic and rapid mental conversion skills.

Given Data / Assumptions:

• Minuend: ACE₁₆.
• Subtrahend: 999₁₆.
• We need the hexadecimal result.

Concept / Approach:
Subtract directly in hex columns or convert to decimal for a quick check. Hex digits A–F represent 10–15. Standard borrowing rules apply in base 16.

Step-by-Step Solution:
Convert to decimal for a check: ACE₁₆ = 1016^2 + 1216 + 14 = 2560 + 192 + 14 = 2766.999₁₆ = 916^2 + 916 + 9 = 2304 + 144 + 9 = 2457.Subtract: 2766 − 2457 = 309.Convert 309 to hex: 309 / 16 = 19 remainder 5; 19 / 16 = 1 remainder 3; 1 / 16 = 0 remainder 1 → 0x135.

Verification / Alternative check:
Column subtraction in hex: E−9 → borrow → 5, C−9 with borrow → 3, A−9 with borrow → 1, yielding 0x135. Matches the decimal cross-check.

Why Other Options Are Wrong:
23516, 03516, 33516, 12516: Each differs by one nibble or digit; none equal 0x135 (decimal 309).

Common Pitfalls:
Forgetting that borrowing in hex subtracts 16 (not 10) and misreading A=10, C=12, E=14.

Final Answer:
13516