Hexadecimal arithmetic practice: Compute the sum of the hexadecimal numbers 0110₁₆ and 10010₁₆. Choose the correct hexadecimal result.

Introduction / Context:Hexadecimal (base-16) arithmetic is widely used for addressing, memory dumps, and low-level debugging. Adding hex numbers follows the same column-wise carry rules as decimal addition, with digits 0–9 and A–F representing values 10–15.

Given Data / Assumptions:

• Add 0110₁₆ (which equals 0x110) and 10010₁₆ (which equals 0x10010).
• Perform standard base-16 addition.

Concept / Approach:Align the least significant digits and add column by column, carrying whenever a column sum is 16 or more. Alternatively, convert to decimal, add, and convert back to hex.

Step-by-Step Solution:Write operands aligned: 10010₁₆ + 0110₁₆.Add lower nibbles: 0 + 0 = 0; next: 1 + 1 = 2; next: 0 + 1 = 1; next: 0 + 1 = 1; highest: 1 + 0 = 1.Result reads 10120₁₆.Check by decimal: 0x10010 = 65552, 0x0110 = 272; sum = 65824 = 0x10120.

Verification / Alternative check:Use positional weights: (1×16^4) + (0×16^3) + (1×16^1) = 65536 + 16 = 65552; (1×16^2) + (1×16^4? no) → for 0x110: 1×256 + 1×16 = 272. Sum converts back to 1×16^4 + 0×16^3 + 1×16^2 + 2×16 + 0 → 0x10120.

Why Other Options Are Wrong:10020₁₆ and 11120₁₆ differ in the middle digits, not matching correct column carries.00120₁₆ ignores the higher-order 16^4 term.11020₁₆ introduces an incorrect extra 16^3 term.

Common Pitfalls:Misaligning digits, dropping leading zeros incorrectly, or treating hex digits as decimal.

Final Answer:10120₁₆