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Question

Difficulty: MediumNumber Bases and Conversions

What is the result of the subtraction 5238−2678523_8 - 267_8 in base 8?

  1. 2348234_8Answer
  2. B
    2568256_8
  3. C
    2448244_8
  4. D
    3448344_8

Answer

2348234_8
Performing place-by-place subtraction in base 8 requires borrowing 8 whenever a top digit is smaller than the bottom digit. Borrowing 1 from the tens place adds 8 to the units place (3+8−7=43 + 8 - 7 = 4). The tens place becomes 1, borrowing 1 from the hundreds place adds 8 (1+8−6=31 + 8 - 6 = 3). The hundreds place becomes 4, giving 4−2=24 - 2 = 2. Thus, the answer is 2348234_8.

Step-by-Step Solution

1
Subtract the units column (3−73 - 7 in base 8)
Borrow 11 from the middle column (which represents 88). The units position becomes 3+8=113 + 8 = 11. Then 11−7=411 - 7 = 4.
Since 3<73 < 7, borrowing from the next higher position (base 8) is required.
2
Subtract the middle column (1−61 - 6 in base 8)
After borrowing, the middle digit 22 becomes 11. Borrow 11 from the hundreds column (representing 88). The middle position becomes 1+8=91 + 8 = 9. Then 9−6=39 - 6 = 3.
The middle digit was reduced by 11 due to the previous borrow, requiring another borrow from the left.
3
Subtract the hundreds column (4−24 - 2 in base 8)
The left digit 55 was reduced to 44. Then 4−2=24 - 2 = 2.
Complete the subtraction for the leading column.
4
Combine the resulting digits
2348234_8
Concatenating the results from left to right gives the final answer in base 8.

Key Concept

Subtraction in non-decimal number bases
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Topics

Number Bases and Conversions

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