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:
263
0 262
0 261
0 260
0 259
0 258
0 257
0 256
0 255
0 254
0 253
0 252
0 251
0 250
0 249
0 248
0 247
0 246
0 245
0 244
0 243
0 242
0 241
0 240
0 239
1 238
0 237
0 236
0 235
0 234
0 233
0 232
1 231
0 230
1 229
0 228
0 227
0 226
1 225
0 224
1 223
1 222
0 221
0 220
1 219
0 218
0 217
0 216
0 215
0 214
0 213
1 212
1 211
0 210
0 29
1 28
1 27
1 26
1 25
0 24
1 23
1 22
0 21
1 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
0000 0000 0000 0000 0000 0000 1000 0001 0100 0101 1001 0000 0011 0011 1101 1011(2) =
(0 × 263 + 0 × 262 + 0 × 261 + 0 × 260 + 0 × 259 + 0 × 258 + 0 × 257 + 0 × 256 + 0 × 255 + 0 × 254 + 0 × 253 + 0 × 252 + 0 × 251 + 0 × 250 + 0 × 249 + 0 × 248 + 0 × 247 + 0 × 246 + 0 × 245 + 0 × 244 + 0 × 243 + 0 × 242 + 0 × 241 + 0 × 240 + 1 × 239 + 0 × 238 + 0 × 237 + 0 × 236 + 0 × 235 + 0 × 234 + 0 × 233 + 1 × 232 + 0 × 231 + 1 × 230 + 0 × 229 + 0 × 228 + 0 × 227 + 1 × 226 + 0 × 225 + 1 × 224 + 1 × 223 + 0 × 222 + 0 × 221 + 1 × 220 + 0 × 219 + 0 × 218 + 0 × 217 + 0 × 216 + 0 × 215 + 0 × 214 + 1 × 213 + 1 × 212 + 0 × 211 + 0 × 210 + 1 × 29 + 1 × 28 + 1 × 27 + 1 × 26 + 0 × 25 + 1 × 24 + 1 × 23 + 0 × 22 + 1 × 21 + 1 × 20)(10) =
(0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 549 755 813 888 + 0 + 0 + 0 + 0 + 0 + 0 + 4 294 967 296 + 0 + 1 073 741 824 + 0 + 0 + 0 + 67 108 864 + 0 + 16 777 216 + 8 388 608 + 0 + 0 + 1 048 576 + 0 + 0 + 0 + 0 + 0 + 0 + 8 192 + 4 096 + 0 + 0 + 512 + 256 + 128 + 64 + 0 + 16 + 8 + 0 + 2 + 1)(10) =
(549 755 813 888 + 4 294 967 296 + 1 073 741 824 + 67 108 864 + 16 777 216 + 8 388 608 + 1 048 576 + 8 192 + 4 096 + 512 + 256 + 128 + 64 + 16 + 8 + 2 + 1)(10) =
555 217 859 547(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0000 0000 0000 0000 0000 0000 1000 0001 0100 0101 1001 0000 0011 0011 1101 1011(2) = 555 217 859 547(10)
The signed binary number in one's complement representation 0000 0000 0000 0000 0000 0000 1000 0001 0100 0101 1001 0000 0011 0011 1101 1011(2) converted and written as an integer in decimal system (base ten):
0000 0000 0000 0000 0000 0000 1000 0001 0100 0101 1001 0000 0011 0011 1101 1011(2) = 555 217 859 547(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.