1. Is this a positive or a negative number?
1000 1001 is the binary representation of a negative integer, on 8 bits.
In a signed binary in two's complement representation, the first bit (the leftmost) indicates the sign, 1 = negative, 0 = positive.
2. Get the binary representation in one's complement.
* Run this step only if the number is negative *
Note on binary subtraction rules:
11 - 1 = 10; 10 - 1 = 1; 1 - 0 = 1; 1 - 1 = 0.
Subtract 1 from the initial binary number.
1000 1001 - 1 = 1000 1000
3. Get the binary representation of the positive (unsigned) number.
* Run this step only if the number is negative *
Flip all the bits of the signed binary in one's complement representation (reverse the digits) - replace the bits set on 1 with 0s and the bits on 0 with 1s:
!(1000 1000) = 0111 0111
4. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
27
0 26
1 25
1 24
1 23
0 22
1 21
1 20
1
1000 1001(2) = -119(10)
The signed binary number in two's complement representation 1000 1001(2) converted and written as an integer in decimal system (base ten):
1000 1001(2) = -119(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.