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
1 254
0 253
1 252
0 251
1 250
1 249
1 248
0 247
1 246
1 245
0 244
0 243
1 242
0 241
1 240
0 239
1 238
1 237
0 236
1 235
0 234
0 233
1 232
0 231
1 230
1 229
0 228
1 227
1 226
0 225
0 224
0 223
0 222
1 221
0 220
0 219
0 218
0 217
0 216
0 215
1 214
1 213
0 212
1 211
0 210
0 29
1 28
0 27
0 26
1 25
1 24
1 23
1 22
1 21
1 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
0000 0000 1010 1110 1100 1010 1101 0010 1101 1000 0100 0000 1101 0010 0111 1111(2) =
(0 × 263 + 0 × 262 + 0 × 261 + 0 × 260 + 0 × 259 + 0 × 258 + 0 × 257 + 0 × 256 + 1 × 255 + 0 × 254 + 1 × 253 + 0 × 252 + 1 × 251 + 1 × 250 + 1 × 249 + 0 × 248 + 1 × 247 + 1 × 246 + 0 × 245 + 0 × 244 + 1 × 243 + 0 × 242 + 1 × 241 + 0 × 240 + 1 × 239 + 1 × 238 + 0 × 237 + 1 × 236 + 0 × 235 + 0 × 234 + 1 × 233 + 0 × 232 + 1 × 231 + 1 × 230 + 0 × 229 + 1 × 228 + 1 × 227 + 0 × 226 + 0 × 225 + 0 × 224 + 0 × 223 + 1 × 222 + 0 × 221 + 0 × 220 + 0 × 219 + 0 × 218 + 0 × 217 + 0 × 216 + 1 × 215 + 1 × 214 + 0 × 213 + 1 × 212 + 0 × 211 + 0 × 210 + 1 × 29 + 0 × 28 + 0 × 27 + 1 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 1 × 20)(10) =
(0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 36 028 797 018 963 968 + 0 + 9 007 199 254 740 992 + 0 + 2 251 799 813 685 248 + 1 125 899 906 842 624 + 562 949 953 421 312 + 0 + 140 737 488 355 328 + 70 368 744 177 664 + 0 + 0 + 8 796 093 022 208 + 0 + 2 199 023 255 552 + 0 + 549 755 813 888 + 274 877 906 944 + 0 + 68 719 476 736 + 0 + 0 + 8 589 934 592 + 0 + 2 147 483 648 + 1 073 741 824 + 0 + 268 435 456 + 134 217 728 + 0 + 0 + 0 + 0 + 4 194 304 + 0 + 0 + 0 + 0 + 0 + 0 + 32 768 + 16 384 + 0 + 4 096 + 0 + 0 + 512 + 0 + 0 + 64 + 32 + 16 + 8 + 4 + 2 + 1)(10) =
(36 028 797 018 963 968 + 9 007 199 254 740 992 + 2 251 799 813 685 248 + 1 125 899 906 842 624 + 562 949 953 421 312 + 140 737 488 355 328 + 70 368 744 177 664 + 8 796 093 022 208 + 2 199 023 255 552 + 549 755 813 888 + 274 877 906 944 + 68 719 476 736 + 8 589 934 592 + 2 147 483 648 + 1 073 741 824 + 268 435 456 + 134 217 728 + 4 194 304 + 32 768 + 16 384 + 4 096 + 512 + 64 + 32 + 16 + 8 + 4 + 2 + 1)(10) =
49 199 652 867 723 903(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0000 0000 1010 1110 1100 1010 1101 0010 1101 1000 0100 0000 1101 0010 0111 1111(2) = 49 199 652 867 723 903(10)
The signed binary number in one's complement representation 0000 0000 1010 1110 1100 1010 1101 0010 1101 1000 0100 0000 1101 0010 0111 1111(2) converted and written as an integer in decimal system (base ten):
0000 0000 1010 1110 1100 1010 1101 0010 1101 1000 0100 0000 1101 0010 0111 1111(2) = 49 199 652 867 723 903(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.