1. Is this a positive or a negative number?
1111 1111 0001 0101 is the binary representation of a negative integer, on 16 bits (2 Bytes).
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.
1111 1111 0001 0101 - 1 = 1111 1111 0001 0100
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:
!(1111 1111 0001 0100) = 0000 0000 1110 1011
4. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
215
0 214
0 213
0 212
0 211
0 210
0 29
0 28
0 27
1 26
1 25
1 24
0 23
1 22
0 21
1 20
1
1111 1111 0001 0101(2) = -235(10)
The signed binary number in two's complement representation 1111 1111 0001 0101(2) converted and written as an integer in decimal system (base ten):
1111 1111 0001 0101(2) = -235(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.