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:
!(1110 0000 1110 1101 0101 1110 1000 1001) = 0001 1111 0001 0010 1010 0001 0111 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
1 227
1 226
1 225
1 224
1 223
0 222
0 221
0 220
1 219
0 218
0 217
1 216
0 215
1 214
0 213
1 212
0 211
0 210
0 29
0 28
1 27
0 26
1 25
1 24
1 23
0 22
1 21
1 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
0001 1111 0001 0010 1010 0001 0111 0110(2) =
(0 × 231 + 0 × 230 + 0 × 229 + 1 × 228 + 1 × 227 + 1 × 226 + 1 × 225 + 1 × 224 + 0 × 223 + 0 × 222 + 0 × 221 + 1 × 220 + 0 × 219 + 0 × 218 + 1 × 217 + 0 × 216 + 1 × 215 + 0 × 214 + 1 × 213 + 0 × 212 + 0 × 211 + 0 × 210 + 0 × 29 + 1 × 28 + 0 × 27 + 1 × 26 + 1 × 25 + 1 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 0 × 20)(10) =
(0 + 0 + 0 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 16 777 216 + 0 + 0 + 0 + 1 048 576 + 0 + 0 + 131 072 + 0 + 32 768 + 0 + 8 192 + 0 + 0 + 0 + 0 + 256 + 0 + 64 + 32 + 16 + 0 + 4 + 2 + 0)(10) =
(268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 16 777 216 + 1 048 576 + 131 072 + 32 768 + 8 192 + 256 + 64 + 32 + 16 + 4 + 2)(10) =
521 314 678(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1110 0000 1110 1101 0101 1110 1000 1001(2) = -521 314 678(10)
The signed binary number in one's complement representation 1110 0000 1110 1101 0101 1110 1000 1001(2) converted and written as an integer in decimal system (base ten):
1110 0000 1110 1101 0101 1110 1000 1001(2) = -521 314 678(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.