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
0 260
0 259
1 258
1 257
0 256
1 255
1 254
0 253
1 252
1 251
1 250
0 249
0 248
0 247
0 246
1 245
1 244
0 243
1 242
0 241
1 240
0 239
0 238
0 237
1 236
1 235
1 234
0 233
0 232
1 231
1 230
1 229
0 228
0 227
0 226
1 225
1 224
0 223
0 222
1 221
0 220
1 219
0 218
0 217
1 216
0 215
1 214
1 213
0 212
0 211
0 210
1 29
1 28
1 27
1 26
1 25
1 24
1 23
1 22
1 21
1 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
0100 1101 1011 1000 0110 1010 0011 1001 1100 0110 0101 0010 1100 0111 1111 1110(2) =
(0 × 263 + 1 × 262 + 0 × 261 + 0 × 260 + 1 × 259 + 1 × 258 + 0 × 257 + 1 × 256 + 1 × 255 + 0 × 254 + 1 × 253 + 1 × 252 + 1 × 251 + 0 × 250 + 0 × 249 + 0 × 248 + 0 × 247 + 1 × 246 + 1 × 245 + 0 × 244 + 1 × 243 + 0 × 242 + 1 × 241 + 0 × 240 + 0 × 239 + 0 × 238 + 1 × 237 + 1 × 236 + 1 × 235 + 0 × 234 + 0 × 233 + 1 × 232 + 1 × 231 + 1 × 230 + 0 × 229 + 0 × 228 + 0 × 227 + 1 × 226 + 1 × 225 + 0 × 224 + 0 × 223 + 1 × 222 + 0 × 221 + 1 × 220 + 0 × 219 + 0 × 218 + 1 × 217 + 0 × 216 + 1 × 215 + 1 × 214 + 0 × 213 + 0 × 212 + 0 × 211 + 1 × 210 + 1 × 29 + 1 × 28 + 1 × 27 + 1 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 0 × 20)(10) =
(0 + 4 611 686 018 427 387 904 + 0 + 0 + 576 460 752 303 423 488 + 288 230 376 151 711 744 + 0 + 72 057 594 037 927 936 + 36 028 797 018 963 968 + 0 + 9 007 199 254 740 992 + 4 503 599 627 370 496 + 2 251 799 813 685 248 + 0 + 0 + 0 + 0 + 70 368 744 177 664 + 35 184 372 088 832 + 0 + 8 796 093 022 208 + 0 + 2 199 023 255 552 + 0 + 0 + 0 + 137 438 953 472 + 68 719 476 736 + 34 359 738 368 + 0 + 0 + 4 294 967 296 + 2 147 483 648 + 1 073 741 824 + 0 + 0 + 0 + 67 108 864 + 33 554 432 + 0 + 0 + 4 194 304 + 0 + 1 048 576 + 0 + 0 + 131 072 + 0 + 32 768 + 16 384 + 0 + 0 + 0 + 1 024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 0)(10) =
(4 611 686 018 427 387 904 + 576 460 752 303 423 488 + 288 230 376 151 711 744 + 72 057 594 037 927 936 + 36 028 797 018 963 968 + 9 007 199 254 740 992 + 4 503 599 627 370 496 + 2 251 799 813 685 248 + 70 368 744 177 664 + 35 184 372 088 832 + 8 796 093 022 208 + 2 199 023 255 552 + 137 438 953 472 + 68 719 476 736 + 34 359 738 368 + 4 294 967 296 + 2 147 483 648 + 1 073 741 824 + 67 108 864 + 33 554 432 + 4 194 304 + 1 048 576 + 131 072 + 32 768 + 16 384 + 1 024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2)(10) =
5 600 342 933 008 205 822(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0100 1101 1011 1000 0110 1010 0011 1001 1100 0110 0101 0010 1100 0111 1111 1110(2) = 5 600 342 933 008 205 822(10)
The signed binary number in one's complement representation 0100 1101 1011 1000 0110 1010 0011 1001 1100 0110 0101 0010 1100 0111 1111 1110(2) converted and written as an integer in decimal system (base ten):
0100 1101 1011 1000 0110 1010 0011 1001 1100 0110 0101 0010 1100 0111 1111 1110(2) = 5 600 342 933 008 205 822(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.