Decimal-to-hexadecimal conversion Convert the decimal number 457₁₀ to hexadecimal (base 16).
Electronics
Number Systems and Codes
Difficulty: Easy
Choose an option
-
A711
-
B2C7
-
C811
-
D1C9
Answer
Correct Answer: 1C9
Explanation
Introduction / Context:Converting from decimal to hexadecimal can be done by repeated division by 16, recording remainders as hex digits (0–9, A–F).
Given Data / Assumptions:
- Decimal number: 457.
- Hex base: 16, digits A=10, B=11, C=12, D=13, E=14, F=15.
Concept / Approach:Use successive division by 16 and collect remainders from last to first to form the hex representation.
Step-by-Step Solution:
1) 457 / 16 = 28 remainder 9 → least significant digit 9.2) 28 / 16 = 1 remainder 12 → next digit C.3) 1 / 16 = 0 remainder 1 → most significant digit 1.4) Combine MSB→LSB: 1 C 9 → 1C9₁₆.Verification / Alternative check:Compute back: 1*16^2 + C(12)*16 + 9 = 256 + 192 + 9 = 457.
Why Other Options Are Wrong:
- 711/2C7/811: Do not evaluate to 457 when converted back.
Common Pitfalls:Writing remainders in the wrong order or misreading C as 11 instead of 12.
Final Answer:1C9