# Homework Help: Is the answer in book wrong? Ones complement conversion

1. Sep 11, 2014

### orangeincup

1. The problem statement, all variables and given/known data
Convert the following one's compliment binary into a decimal number
1000 1000

3. The attempt at a solution
The book says the answer is suppose to be 119, but shouldn't it be negative? I thought one at the front of the number represented the sign, when using one's compliment.

Last edited: Sep 11, 2014
2. Sep 11, 2014

### Staff: Mentor

It depends on how many bits are defined for the number like 8bits or 16bits...

In this case, it looks like it is a negative number so the ones complement of it will be positive because all bits are reversed.

So show your work and we can confirm what you got.

http://en.m.wikipedia.org/wiki/Ones'_complement

Last edited: Sep 11, 2014
3. Sep 11, 2014

### rcgldr

For positive numbers, the ones and twos complement representation of a value are the same. For negative numbers with the same string of bits, the ones complement value will be +1 more than the two's complement value. For 8 bit numbers, 10000000 is -128 in two's complement and -127 (= -128 + 1) in one's complement, 11111111 is -1 in two's complement and 0 (= -1 + 1) in ones complement, and 10001000 is -120 in two's complement and -119 (= -120 + 1) in ones compement.

Last edited: Sep 11, 2014
4. Sep 11, 2014

### orangeincup

1000 1000 represented by one's complement
My workings...
1 at the far right means it's negative
inverting numbers...
0111 0111
0+64+32+16+0+4+2+1=119

Answer: -119

The solution says it's 119. Here's exactly what the question asks for:

What is the decimal representation of 8 bit 1000 1000 (subscript 2) one’s
compliment numbers.
Ans: 119

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