Number Systems — Convert 15,536 (Decimal) to Hexadecimal Find the hexadecimal equivalent of the decimal number 15,536, showing the place-value reasoning.

Introduction / Context:
Converting from decimal to hexadecimal is routine in digital systems when addressing memory, reading registers, or interpreting dumps. Hexadecimal condenses binary into human-friendly base-16 digits using 0–9 and A–F, where A=10 through F=15.

Given Data / Assumptions:

• Decimal input: 15,536.
• Hexadecimal base: 16 with weights 16^0, 16^1, 16^2, 16^3, ...
• No sign or fractional component.

Concept / Approach:
Use positional weights or repeated division by 16. For a four-digit hex result H3 H2 H1 H0, the decimal value is H316^3 + H216^2 + H116^1 + H016^0. Determine each digit by dividing and taking remainders in base 16.

Step-by-Step Solution:
Compute 16^3 = 4096 and 16^2 = 256.Find H3: floor(15,536 / 4096) = 3 → remainder = 15,536 − 34096 = 15,536 − 12,288 = 3,248.Find H2: floor(3,248 / 256) = 12 → 12 maps to C; remainder = 3,248 − 12256 = 3,248 − 3,072 = 176.Find H1: floor(176 / 16) = 11 → 11 maps to B; remainder = 176 − 1116 = 176 − 176 = 0.Find H0: remainder 0 → 0.Assemble digits: 3 C B 0 → 3CB0.

Verification / Alternative check:
Back-convert: 34096 + C256 + B16 + 0 = 12,288 + 3,072 + 176 + 0 = 15,536, confirming correctness.

Why Other Options Are Wrong:

• 3C66, 63C0, 6300: Each changes one or more hex digits; back-conversion does not equal 15,536.

Common Pitfalls:
Mis-mapping letters (e.g., confusing B=11 and C=12) or forgetting to carry remainders properly during division by 16.

Final Answer:
3CB0