1. Is this a positive or a negative number?
0100 0001 0000 0000 is the binary representation of a positive integer, on 16 bits (2 Bytes).
In a signed binary in one's complement representation, the first bit (the leftmost) indicates the sign, 1 = negative, 0 = positive.
2. 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:
* Not the case - the number is positive *
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
215
0 214
1 213
0 212
0 211
0 210
0 29
0 28
1 27
0 26
0 25
0 24
0 23
0 22
0 21
0 20
0
The signed binary number in one's complement representation 0100 0001 0000 0000(2) converted and written as an integer in decimal system (base ten):
0100 0001 0000 0000(2) = 16 640(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.