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GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 17

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Consider the bit pattern $10110110.$ Interpret this bit pattern as a $8$-bit $2$'s complement number. What is the largest magnitude negative number that can be added to this value without causing $8$-bit $2$'s complement overflow? (Write your answer in decimal, only the magnitude, not the sign)
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The decimal value of $2$'s complement number $10110110$ is $-74.$

We want to add up to the largest magnitude negative number that can be expressed in $8$-bit $2$ 's complement, namely $-2^7 =-128$.

So the answer is $-128-(-74)=-54$.

The answer without a sign is $54.$
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