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Overflow occurs if what bits are required to contain the result from an N-bit addition or subtraction

Question

Overflow occurs if what bits are required to contain the result from an N-bit addition or subtraction

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Solution

Overflow occurs when more than N bits are required to contain the result from an N-bit addition or subtraction.

Here are the steps to understand this:

  1. Consider two N-bit numbers. The maximum value they can represent is when all bits are 1.

  2. If you add these two numbers, the result can be a number that requires N+1 bits to represent. This is because the sum of the two maximum N-bit numbers is a number that is larger than the maximum N-bit number.

  3. Similarly, if you subtract the smallest possible N-bit number (which is zero if we're considering unsigned numbers) from the largest possible N-bit number, the result is still an N-bit number.

  4. However, if we're considering signed numbers and you subtract the smallest possible N-bit number from the largest possible N-bit number, the result can be a number that requires N+1 bits to represent. This is because the difference between the two extreme N-bit numbers is a number that is larger than the maximum N-bit number.

  5. In both these cases, if the system can only accommodate N bits for the result, an overflow occurs. This is because the result requires more bits than the system can provide.

  6. Therefore, overflow occurs when more than N bits are required to contain the result from an N-bit addition or subtraction.

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