Decimal to hexadecimal conversion Convert the decimal number 125 to base-16 (hexadecimal).
Electronics
Number Systems and Codes
Difficulty: Easy
Choose an option
-
A7D₁₆
-
BD7₁₆
-
C7C₁₆
-
DC7₁₆
Answer
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