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
0 238
0 237
0 236
0 235
0 234
1 233
1 232
0 231
1 230
0 229
1 228
1 227
1 226
0 225
0 224
1 223
1 222
0 221
1 220
1 219
0 218
1 217
1 216
1 215
0 214
0 213
1 212
1 211
0 210
1 29
1 28
0 27
0 26
1 25
1 24
0 23
0 22
0 21
0 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
0000 0000 0000 0000 0000 0000 0000 0110 1011 1001 1011 0111 0011 0110 0110 0001(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 + 0 × 239 + 0 × 238 + 0 × 237 + 0 × 236 + 0 × 235 + 1 × 234 + 1 × 233 + 0 × 232 + 1 × 231 + 0 × 230 + 1 × 229 + 1 × 228 + 1 × 227 + 0 × 226 + 0 × 225 + 1 × 224 + 1 × 223 + 0 × 222 + 1 × 221 + 1 × 220 + 0 × 219 + 1 × 218 + 1 × 217 + 1 × 216 + 0 × 215 + 0 × 214 + 1 × 213 + 1 × 212 + 0 × 211 + 1 × 210 + 1 × 29 + 0 × 28 + 0 × 27 + 1 × 26 + 1 × 25 + 0 × 24 + 0 × 23 + 0 × 22 + 0 × 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 + 0 + 0 + 0 + 0 + 0 + 17 179 869 184 + 8 589 934 592 + 0 + 2 147 483 648 + 0 + 536 870 912 + 268 435 456 + 134 217 728 + 0 + 0 + 16 777 216 + 8 388 608 + 0 + 2 097 152 + 1 048 576 + 0 + 262 144 + 131 072 + 65 536 + 0 + 0 + 8 192 + 4 096 + 0 + 1 024 + 512 + 0 + 0 + 64 + 32 + 0 + 0 + 0 + 0 + 1)(10) =
(17 179 869 184 + 8 589 934 592 + 2 147 483 648 + 536 870 912 + 268 435 456 + 134 217 728 + 16 777 216 + 8 388 608 + 2 097 152 + 1 048 576 + 262 144 + 131 072 + 65 536 + 8 192 + 4 096 + 1 024 + 512 + 64 + 32 + 1)(10) =
28 885 595 745(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 0000 0110 1011 1001 1011 0111 0011 0110 0110 0001(2) = 28 885 595 745(10)
The signed binary number in one's complement representation 0000 0000 0000 0000 0000 0000 0000 0110 1011 1001 1011 0111 0011 0110 0110 0001(2) converted and written as an integer in decimal system (base ten):
0000 0000 0000 0000 0000 0000 0000 0110 1011 1001 1011 0111 0011 0110 0110 0001(2) = 28 885 595 745(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.