Question
Consider the equation: , where stands for to the base . Find .
Official answer and solution
- Official answer
- C
- From
- Official GATE 2014 answer key
Solution
Isolate Y and perform base-8 (octal) subtraction column by column with borrows.
Given the octal equation:
Perform subtraction column by column from right to left (base 8):
-
Position 0 (units):
-
Position 1 (eights):
, so borrow from the next position (worth in base 8). -
Position 2 (sixty-fours):
becomes after lending the borrow. -
Position 3 (five-hundred-twelves):
Combining the digits gives:
This matches option C.
C
Borrowing 10 instead of 8 when subtracting in base 8.
The answer is the one in the official GATE answer key. The solution is this site's own explanation.
Source
- Paper
- GATE 2014 Computer Science and Information Technology (CS) Session 3
- Question
- 10 of 65, printed as GA Q.10
- Section
- General Aptitude
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