Decimal to hexadecimal conversion — Convert the base-10 number 5238 into base 16 (hexadecimal). Provide the correct hexadecimal representation.

Introduction:Converting decimal integers to hexadecimal is routine when working with memory addresses, register values, and encoded data. Performing the conversion by repeated division by 16 builds intuition for positional weights and helps verify tool outputs during debugging.

Given Data / Assumptions:

• Decimal value N = 5238.
• Hexadecimal base B = 16; digits 0–9 and A–F represent 10–15.
• We assume an integer without fractional part.

Concept / Approach:

Use successive division by 16 to obtain remainders (least significant digit first). The quotient becomes the new dividend. Stop when the quotient is zero. Then write the remainders in reverse order to form the hexadecimal number.

Step-by-Step Solution:

Verification / Alternative check:

Expand to decimal: 116^3 + 416^2 + 7*16 + 6 = 4096 + 1024 + 112 + 6 = 5238, confirming correctness.

Why Other Options Are Wrong:

• 327.375: A decimal/hex mixed form; not a proper integer hex representation.
• 12166 / 1388: Decimal-like strings that do not correspond to 5238 in hex.
• 0x1476: Correct value but includes a programming prefix; the expected answer is the bare hexadecimal digits.

Common Pitfalls:

• Writing remainders in the wrong order; always reverse the remainder sequence.
• Confusing decimal digits with hex digits A–F when remainders exceed 9 (not encountered here but common elsewhere).

Final Answer:

1476