What is the result of the subtraction 524_8 - 267_8 expressed in base 8? — JAMB UTME

What is the result of the subtraction $524_8 - 267_8$ expressed in base 8?

$235_8$ Answer
B
$257_8$
C
$345_8$
D
$343_8$

Answer

The correct answer is

235_8

Subtracting

267_8

from

524_8

using direct base-8 subtraction requires borrowing 8 when a digit is smaller than the digit subtracted from it. In the units column, borrowing 1 (which equals 8) gives

(4 + 8) - 7 = 5

. In the eights column, the borrowed-from digit 2 becomes 1; borrowing 1 (which equals 8) gives

(1 + 8) - 6 = 3

. In the sixty-fours column, the borrowed-from digit 5 becomes 4;

4 - 2 = 2

. Thus, the difference is

235_8

Step-by-Step Solution

Convert both octal numbers to base 10.

524_8 = (5 \times 8^2) + (2 \times 8^1) + (4 \times 8^0) = 320 + 16 + 4 = 340_{10}

, and

267_8 = (2 \times 8^2) + (6 \times 8^1) + (7 \times 8^0) = 128 + 48 + 7 = 183_{10}

Converting to decimal simplifies standard arithmetic operations.

Subtract the decimal values.

340_{10} - 183_{10} = 157_{10}

Obtain the difference in base 10.

Convert the decimal difference

157_{10}

back to base 8.

157 \div 8 = 19

remainder

5

;

19 \div 8 = 2

remainder

3

;

2 \div 8 = 0

remainder

2

. Reading remainders from bottom to top gives

235_8

Successive division by 8 yields the octal representation.

Key Concept

Non-decimal base arithmetic and borrowing rules

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