a) An overflow occurs when the result of adding two number islarger than can be

Question

a) An overflow occurs when the result of adding two number islarger than can be represented. for example, two 4-bit signednumbers will cause an overflow if their result is greater than +7or less than -8. For example, the following additions will cause anoverflow because their results are outside the range. So, if4-bit addition is performed on these numbers, what will the resultbe interpreted as?
6+6      -7+-3

b) How can someone detect an overflow condition during a 4-bitaddition by examining the sign bits of the two inputs and theresult?

Explanation / Answer

a) 6 + 6 =12 but 12 cannot be represented in 4 bits. SO the result will be-4 due to the overflow 6 in binary = 0110 0110 + 0110 = 1100 1100 is -4 in binary -7 = 1001 -3 = 1101 1001 +1101 = 0110 and overflow is ignored. 0110 is +6 in binary . So the result will be +6 due to oveflow. b) While adding, the numbers are assumed to be of thesame sign . If the signs are different, then it is calledsubtraction. So, if the result has the same sign bit as the 2 numbers whichwere added, then there has been no overflow. If the result has a different sign bit from the 2 numbers,then an overflow has occured. I hope this helps you

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