1. Is this a positive or a negative number?
0000 0000 0000 0001 1111 1000 1101 1101 0011 1010 1111 1110 0001 0011 1111 0011 is the binary representation of a positive integer, on 64 bits (8 Bytes).
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
1 247
1 246
1 245
1 244
1 243
1 242
0 241
0 240
0 239
1 238
1 237
0 236
1 235
1 234
1 233
0 232
1 231
0 230
0 229
1 228
1 227
1 226
0 225
1 224
0 223
1 222
1 221
1 220
1 219
1 218
1 217
1 216
0 215
0 214
0 213
0 212
1 211
0 210
0 29
1 28
1 27
1 26
1 25
1 24
1 23
0 22
0 21
1 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
0000 0000 0000 0001 1111 1000 1101 1101 0011 1010 1111 1110 0001 0011 1111 0011(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 + 1 × 248 + 1 × 247 + 1 × 246 + 1 × 245 + 1 × 244 + 1 × 243 + 0 × 242 + 0 × 241 + 0 × 240 + 1 × 239 + 1 × 238 + 0 × 237 + 1 × 236 + 1 × 235 + 1 × 234 + 0 × 233 + 1 × 232 + 0 × 231 + 0 × 230 + 1 × 229 + 1 × 228 + 1 × 227 + 0 × 226 + 1 × 225 + 0 × 224 + 1 × 223 + 1 × 222 + 1 × 221 + 1 × 220 + 1 × 219 + 1 × 218 + 1 × 217 + 0 × 216 + 0 × 215 + 0 × 214 + 0 × 213 + 1 × 212 + 0 × 211 + 0 × 210 + 1 × 29 + 1 × 28 + 1 × 27 + 1 × 26 + 1 × 25 + 1 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 1 × 20)(10) =
(0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 281 474 976 710 656 + 140 737 488 355 328 + 70 368 744 177 664 + 35 184 372 088 832 + 17 592 186 044 416 + 8 796 093 022 208 + 0 + 0 + 0 + 549 755 813 888 + 274 877 906 944 + 0 + 68 719 476 736 + 34 359 738 368 + 17 179 869 184 + 0 + 4 294 967 296 + 0 + 0 + 536 870 912 + 268 435 456 + 134 217 728 + 0 + 33 554 432 + 0 + 8 388 608 + 4 194 304 + 2 097 152 + 1 048 576 + 524 288 + 262 144 + 131 072 + 0 + 0 + 0 + 0 + 4 096 + 0 + 0 + 512 + 256 + 128 + 64 + 32 + 16 + 0 + 0 + 2 + 1)(10) =
(281 474 976 710 656 + 140 737 488 355 328 + 70 368 744 177 664 + 35 184 372 088 832 + 17 592 186 044 416 + 8 796 093 022 208 + 549 755 813 888 + 274 877 906 944 + 68 719 476 736 + 34 359 738 368 + 17 179 869 184 + 4 294 967 296 + 536 870 912 + 268 435 456 + 134 217 728 + 33 554 432 + 8 388 608 + 4 194 304 + 2 097 152 + 1 048 576 + 524 288 + 262 144 + 131 072 + 4 096 + 512 + 256 + 128 + 64 + 32 + 16 + 2 + 1)(10) =
555 104 037 901 299(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0000 0000 0000 0001 1111 1000 1101 1101 0011 1010 1111 1110 0001 0011 1111 0011(2) = 555 104 037 901 299(10)
The signed binary number in one's complement representation 0000 0000 0000 0001 1111 1000 1101 1101 0011 1010 1111 1110 0001 0011 1111 0011(2) converted and written as an integer in decimal system (base ten):
0000 0000 0000 0001 1111 1000 1101 1101 0011 1010 1111 1110 0001 0011 1111 0011(2) = 555 104 037 901 299(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.