Decimal to octal conversion Convert the decimal number 281 to base-8 (octal).
Electronics
Number Systems and Codes
Difficulty: Easy
Choose an option
-
A134₈
-
B431₈
-
C331₈
-
D133₈
Answer
Correct Answer: 431₈
Explanation
Introduction / Context:Converting from decimal to octal is done by repeated division by 8 and collecting remainders. Reading the remainders backward gives the octal digits.
Given Data / Assumptions:
- Number: 281 (base 10).
- Target base: 8.
Concept / Approach:Use integer division by 8. Each remainder is a base-8 digit from 0 to 7. Stop when the quotient reaches 0, then write remainders from last to first.
Step-by-Step Solution:
1) 281 / 8 → quotient 35, remainder 1 (LSB).2) 35 / 8 → quotient 4, remainder 3.3) 4 / 8 → quotient 0, remainder 4 (MSB).4) Read remainders MSB→LSB: 4 3 1 → 431₈.Verification / Alternative check:Convert back: 48^2 + 38 + 1 = 256 + 24 + 1 = 281, confirming correctness.
Why Other Options Are Wrong:
- 134₈ / 331₈ / 133₈: These evaluate to 92, 217, and 91 respectively, not 281.
Common Pitfalls:Writing the remainders in forward order instead of reverse, or using base-10 powers instead of base-8.
Final Answer:431₈