1. Is this a positive or a negative number?
0000 0000 0000 0000 0000 0000 0001 0101 1110 1100 1111 0110 0001 1110 0111 1111 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
0 247
0 246
0 245
0 244
0 243
0 242
0 241
0 240
0 239
0 238
0 237
0 236
1 235
0 234
1 233
0 232
1 231
1 230
1 229
1 228
0 227
1 226
1 225
0 224
0 223
1 222
1 221
1 220
1 219
0 218
1 217
1 216
0 215
0 214
0 213
0 212
1 211
1 210
1 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 0000 0000 0000 0000 0001 0101 1110 1100 1111 0110 0001 1110 0111 1111(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 + 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 + 0 × 235 + 1 × 234 + 0 × 233 + 1 × 232 + 1 × 231 + 1 × 230 + 1 × 229 + 0 × 228 + 1 × 227 + 1 × 226 + 0 × 225 + 0 × 224 + 1 × 223 + 1 × 222 + 1 × 221 + 1 × 220 + 0 × 219 + 1 × 218 + 1 × 217 + 0 × 216 + 0 × 215 + 0 × 214 + 0 × 213 + 1 × 212 + 1 × 211 + 1 × 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 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 68 719 476 736 + 0 + 17 179 869 184 + 0 + 4 294 967 296 + 2 147 483 648 + 1 073 741 824 + 536 870 912 + 0 + 134 217 728 + 67 108 864 + 0 + 0 + 8 388 608 + 4 194 304 + 2 097 152 + 1 048 576 + 0 + 262 144 + 131 072 + 0 + 0 + 0 + 0 + 4 096 + 2 048 + 1 024 + 512 + 0 + 0 + 64 + 32 + 16 + 8 + 4 + 2 + 1)(10) =
(68 719 476 736 + 17 179 869 184 + 4 294 967 296 + 2 147 483 648 + 1 073 741 824 + 536 870 912 + 134 217 728 + 67 108 864 + 8 388 608 + 4 194 304 + 2 097 152 + 1 048 576 + 262 144 + 131 072 + 4 096 + 2 048 + 1 024 + 512 + 64 + 32 + 16 + 8 + 4 + 2 + 1)(10) =
94 169 865 855(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0000 0000 0000 0000 0000 0000 0001 0101 1110 1100 1111 0110 0001 1110 0111 1111(2) = 94 169 865 855(10)
The signed binary number in one's complement representation 0000 0000 0000 0000 0000 0000 0001 0101 1110 1100 1111 0110 0001 1110 0111 1111(2) converted and written as an integer in decimal system (base ten):
0000 0000 0000 0000 0000 0000 0001 0101 1110 1100 1111 0110 0001 1110 0111 1111(2) = 94 169 865 855(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.