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There is an 8-bit numerical value, where a negative number is represented in two’s complement. When this value is represented in decimal, it becomes -100. When this value is regarded as an unsigned number, which of the following is the correct value in decimal?

First, I have to calculate the decimal 100 in binary, and add the signed bit at the start :

1110 0100

Then, to get the non-negative decimal value of the object, I convert the two complement back to its original value :

0001 1100

which gives me the result is 28

But the correct answer is 156, this is the value I will get if I did not replace the MSB (1) with (0) when converting the two complement back to the original value

1001 1100

What am I missing here?

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    $\begingroup$ The 2's compliment representation of -100 is 1001 1100 and not 1110 0100 $\endgroup$
    – Parth Thakkar
    Oct 16, 2014 at 8:07
  • $\begingroup$ @ParthThakkar You are right, I misunderstood the question, so silly of me! $\endgroup$
    – f855a864
    Oct 16, 2014 at 8:11

1 Answer 1

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First consider the decimal number 100. Binary notation of 100 would be

01100100

Applying the two's complement, we find that -100 must be

10011011 + 00000001 = 10011100

Assuming now this is unsigned, we get $128+16+8+4=156$

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