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
1 259
1 258
0 257
0 256
0 255
0 254
1 253
0 252
1 251
0 250
1 249
1 248
0 247
1 246
0 245
0 244
0 243
0 242
0 241
0 240
1 239
1 238
0 237
0 236
1 235
1 234
1 233
0 232
0 231
0 230
0 229
0 228
0 227
1 226
1 225
0 224
0 223
0 222
0 221
0 220
1 219
0 218
0 217
0 216
0 215
1 214
0 213
1 212
0 211
0 210
0 29
0 28
0 27
0 26
1 25
1 24
1 23
1 22
1 21
0 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
0001 1000 0101 0110 1000 0001 1001 1100 0000 1100 0001 0000 1010 0000 0111 1101(2) =
(0 × 263 + 0 × 262 + 0 × 261 + 1 × 260 + 1 × 259 + 0 × 258 + 0 × 257 + 0 × 256 + 0 × 255 + 1 × 254 + 0 × 253 + 1 × 252 + 0 × 251 + 1 × 250 + 1 × 249 + 0 × 248 + 1 × 247 + 0 × 246 + 0 × 245 + 0 × 244 + 0 × 243 + 0 × 242 + 0 × 241 + 1 × 240 + 1 × 239 + 0 × 238 + 0 × 237 + 1 × 236 + 1 × 235 + 1 × 234 + 0 × 233 + 0 × 232 + 0 × 231 + 0 × 230 + 0 × 229 + 0 × 228 + 1 × 227 + 1 × 226 + 0 × 225 + 0 × 224 + 0 × 223 + 0 × 222 + 0 × 221 + 1 × 220 + 0 × 219 + 0 × 218 + 0 × 217 + 0 × 216 + 1 × 215 + 0 × 214 + 1 × 213 + 0 × 212 + 0 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 1 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20)(10) =
(0 + 0 + 0 + 1 152 921 504 606 846 976 + 576 460 752 303 423 488 + 0 + 0 + 0 + 0 + 18 014 398 509 481 984 + 0 + 4 503 599 627 370 496 + 0 + 1 125 899 906 842 624 + 562 949 953 421 312 + 0 + 140 737 488 355 328 + 0 + 0 + 0 + 0 + 0 + 0 + 1 099 511 627 776 + 549 755 813 888 + 0 + 0 + 68 719 476 736 + 34 359 738 368 + 17 179 869 184 + 0 + 0 + 0 + 0 + 0 + 0 + 134 217 728 + 67 108 864 + 0 + 0 + 0 + 0 + 0 + 1 048 576 + 0 + 0 + 0 + 0 + 32 768 + 0 + 8 192 + 0 + 0 + 0 + 0 + 0 + 0 + 64 + 32 + 16 + 8 + 4 + 0 + 1)(10) =
(1 152 921 504 606 846 976 + 576 460 752 303 423 488 + 18 014 398 509 481 984 + 4 503 599 627 370 496 + 1 125 899 906 842 624 + 562 949 953 421 312 + 140 737 488 355 328 + 1 099 511 627 776 + 549 755 813 888 + 68 719 476 736 + 34 359 738 368 + 17 179 869 184 + 134 217 728 + 67 108 864 + 1 048 576 + 32 768 + 8 192 + 64 + 32 + 16 + 8 + 4 + 1)(10) =
1 753 731 612 124 684 413(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0001 1000 0101 0110 1000 0001 1001 1100 0000 1100 0001 0000 1010 0000 0111 1101(2) = 1 753 731 612 124 684 413(10)
The signed binary number in one's complement representation 0001 1000 0101 0110 1000 0001 1001 1100 0000 1100 0001 0000 1010 0000 0111 1101(2) converted and written as an integer in decimal system (base ten):
0001 1000 0101 0110 1000 0001 1001 1100 0000 1100 0001 0000 1010 0000 0111 1101(2) = 1 753 731 612 124 684 413(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.