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
1 261
1 260
1 259
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
1 236
1 235
1 234
1 233
1 232
1 231
1 230
0 229
0 228
1 227
1 226
1 225
1 224
1 223
1 222
1 221
1 220
0 219
1 218
0 217
0 216
0 215
1 214
1 213
1 212
1 211
0 210
0 29
0 28
0 27
0 26
0 25
0 24
1 23
1 22
0 21
0 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
0111 0000 0000 0000 0000 0000 0011 1111 1001 1111 1110 1000 1111 0000 0001 1000(2) =
(0 × 263 + 1 × 262 + 1 × 261 + 1 × 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 + 1 × 237 + 1 × 236 + 1 × 235 + 1 × 234 + 1 × 233 + 1 × 232 + 1 × 231 + 0 × 230 + 0 × 229 + 1 × 228 + 1 × 227 + 1 × 226 + 1 × 225 + 1 × 224 + 1 × 223 + 1 × 222 + 1 × 221 + 0 × 220 + 1 × 219 + 0 × 218 + 0 × 217 + 0 × 216 + 1 × 215 + 1 × 214 + 1 × 213 + 1 × 212 + 0 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 0 × 26 + 0 × 25 + 1 × 24 + 1 × 23 + 0 × 22 + 0 × 21 + 0 × 20)(10) =
(0 + 4 611 686 018 427 387 904 + 2 305 843 009 213 693 952 + 1 152 921 504 606 846 976 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 137 438 953 472 + 68 719 476 736 + 34 359 738 368 + 17 179 869 184 + 8 589 934 592 + 4 294 967 296 + 2 147 483 648 + 0 + 0 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 16 777 216 + 8 388 608 + 4 194 304 + 2 097 152 + 0 + 524 288 + 0 + 0 + 0 + 32 768 + 16 384 + 8 192 + 4 096 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 16 + 8 + 0 + 0 + 0)(10) =
(4 611 686 018 427 387 904 + 2 305 843 009 213 693 952 + 1 152 921 504 606 846 976 + 137 438 953 472 + 68 719 476 736 + 34 359 738 368 + 17 179 869 184 + 8 589 934 592 + 4 294 967 296 + 2 147 483 648 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 16 777 216 + 8 388 608 + 4 194 304 + 2 097 152 + 524 288 + 32 768 + 16 384 + 8 192 + 4 096 + 16 + 8)(10) =
8 070 450 805 513 711 640(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0111 0000 0000 0000 0000 0000 0011 1111 1001 1111 1110 1000 1111 0000 0001 1000(2) = 8 070 450 805 513 711 640(10)
The signed binary number in one's complement representation 0111 0000 0000 0000 0000 0000 0011 1111 1001 1111 1110 1000 1111 0000 0001 1000(2) converted and written as an integer in decimal system (base ten):
0111 0000 0000 0000 0000 0000 0011 1111 1001 1111 1110 1000 1111 0000 0001 1000(2) = 8 070 450 805 513 711 640(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.