1. Is this a positive or a negative number?
1111 1001 0101 0010 is the binary representation of a negative 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:
!(1111 1001 0101 0010) = 0000 0110 1010 1101
3. 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
1 29
1 28
0 27
1 26
0 25
1 24
0 23
1 22
1 21
0 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
0000 0110 1010 1101(2) =
(0 × 215 + 0 × 214 + 0 × 213 + 0 × 212 + 0 × 211 + 1 × 210 + 1 × 29 + 0 × 28 + 1 × 27 + 0 × 26 + 1 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20)(10) =
(0 + 0 + 0 + 0 + 0 + 1 024 + 512 + 0 + 128 + 0 + 32 + 0 + 8 + 4 + 0 + 1)(10) =
(1 024 + 512 + 128 + 32 + 8 + 4 + 1)(10) =
1 709(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1111 1001 0101 0010(2) = -1 709(10)
The signed binary number in one's complement representation 1111 1001 0101 0010(2) converted and written as an integer in decimal system (base ten):
1111 1001 0101 0010(2) = -1 709(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.