Number systems: Convert the decimal value 93₁₀ to its hexadecimal (base-16) representation.

Introduction / Context:Base conversion between decimal and hexadecimal is a routine skill in computing, especially for memory addresses, color codes, and low-level debugging. Hexadecimal compresses binary neatly because each hex digit corresponds to 4 binary bits.

Given Data / Assumptions:

• Input value: 93 in base 10.
• Target base: 16 (hexadecimal).
• Standard digit mapping: 10→A, 11→B, 12→C, 13→D, 14→E, 15→F.

Concept / Approach:Use repeated division by 16. The quotient and remainder sequence, read from last remainder to first, gives the hex digits. Alternatively, convert 93 to binary and group bits by 4; the division method is straightforward here.

Step-by-Step Solution:Compute 93 / 16 → quotient = 5, remainder = 13.Map remainder 13 to hex digit D.Write hex as quotient-remainder pair: 5D16.Sanity check: 5 * 16 + 13 = 80 + 13 = 93.

Verification / Alternative check:Binary route: 93₁₀ = 0101 1101₂ → split into nibbles 0101 (5) and 1101 (D) → 5D16.

Why Other Options Are Wrong:2D16: equals 45 in decimal (216 + 13), not 93.6216: equals 98 decimal (616 + 2), not 93.3116: equals 49 decimal (3*16 + 1), not 93.None of the above: incorrect because 5D16 is correct.

Common Pitfalls:Mis-mapping remainders 10–15 to A–F and reversing the quotient/remainder order.

Final Answer:5D16