Decimal to hexadecimal conversion Convert the decimal number 125 to base-16 (hexadecimal).

Difficulty: Easy

Correct Answer: 7D₁₆

Explanation:


Introduction / Context:
Hexadecimal conversion by repeated division is a standard skill in digital systems and computer architecture.


Given Data / Assumptions:

  • Number: 125 (base 10).
  • Hex digits: 0–9 then A=10, B=11, C=12, D=13, E=14, F=15.


Concept / Approach:
Divide by 16, record remainders as hex digits, and read from last to first to form the hexadecimal value.


Step-by-Step Solution:

1) 125 / 16 → quotient 7, remainder 13 (D).2) 7 / 16 → quotient 0, remainder 7.3) Combine remainders MSB→LSB: 7 D → 7D₁₆.


Verification / Alternative check:
Back-convert: 7*16 + 13 = 112 + 13 = 125.


Why Other Options Are Wrong:

  • D7₁₆ / 7C₁₆ / C7₁₆: These correspond to 215, 124, and 199 respectively.


Common Pitfalls:
Reversing the order of remainders or misvaluing D as 11 instead of 13.


Final Answer:
7D₁₆

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