1. Is this a positive or a negative number?
1111 1111 0111 1111 1111 1111 1101 1001 is the binary representation of a negative integer, on 32 bits (4 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 1111 0111 1111 1111 1111 1101 1001) = 0000 0000 1000 0000 0000 0000 0010 0110
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
231
0 230
0 229
0 228
0 227
0 226
0 225
0 224
0 223
1 222
0 221
0 220
0 219
0 218
0 217
0 216
0 215
0 214
0 213
0 212
0 211
0 210
0 29
0 28
0 27
0 26
0 25
1 24
0 23
0 22
1 21
1 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
0000 0000 1000 0000 0000 0000 0010 0110(2) =
(0 × 231 + 0 × 230 + 0 × 229 + 0 × 228 + 0 × 227 + 0 × 226 + 0 × 225 + 0 × 224 + 1 × 223 + 0 × 222 + 0 × 221 + 0 × 220 + 0 × 219 + 0 × 218 + 0 × 217 + 0 × 216 + 0 × 215 + 0 × 214 + 0 × 213 + 0 × 212 + 0 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 0 × 26 + 1 × 25 + 0 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 0 × 20)(10) =
(0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 8 388 608 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 32 + 0 + 0 + 4 + 2 + 0)(10) =
(8 388 608 + 32 + 4 + 2)(10) =
8 388 646(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1111 1111 0111 1111 1111 1111 1101 1001(2) = -8 388 646(10)
The signed binary number in one's complement representation 1111 1111 0111 1111 1111 1111 1101 1001(2) converted and written as an integer in decimal system (base ten):
1111 1111 0111 1111 1111 1111 1101 1001(2) = -8 388 646(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.