Hex arithmetic — add three independent hexadecimal pairs Add the following hex numbers as three separate sums: (3C + 25), (14 + 28), and (3B + DC). Choose the triple that shows all three results in order.

Introduction / Context:
Hexadecimal addition is a routine digital-design skill used in addressing, checksums, and low-level debugging. This problem asks you to compute three independent hex sums and present the answers in order, demonstrating correct base-16 arithmetic and carry handling.

Given Data / Assumptions:

• Sums to compute: (3C + 25), (14 + 28), (3B + DC).
• All values are hexadecimal (base 16).
• Show each result in hex; the last result may exceed 2 hex digits if a carry propagates.

Concept / Approach:

Add digit by digit in base 16, where A=10, B=11, C=12, D=13, E=14, F=15. When a nibble sum is 16 or more, write the low nibble and carry 1 to the next higher nibble. Convert to decimal only if it helps verify reasonableness, then convert back to hex as needed.

Step-by-Step Solution:

Verification / Alternative check:

Quick nibble check: 0x3C + 0x25 → C + 5 = 17 (write 7, carry 1), 3 + 2 + 1 = 6 → 0x61. Similarly, 0x14 + 0x28 = 0x3C. For 0x3B + 0xDC, lower nibble B + C = 11 + 12 = 23 → write 7 carry 1; upper nibble 3 + D + 1 = 3 + 13 + 1 = 17 → write 1 carry 1 to hundreds → 0x117.

Why Other Options Are Wrong:

• 60 3C 116 and 62 3C 118: off by one on each sum due to carry mistakes.
• 61 3D 117: middle sum should be 3C, not 3D.
• 5F 41 0F5: multiple digit errors and mis-handled carries.

Common Pitfalls:

• Treating hex digits as decimal when carrying.
• Forgetting that 0xF + 0x1 = 0x10 produces a new hex digit.

Final Answer:

61 3C 117