1. Is this a positive or a negative number?
0010 1111 0001 1111 0000 0001 0000 0000 0000 0000 0000 0000 0000 0000 0001 0010 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
1 260
0 259
1 258
1 257
1 256
1 255
0 254
0 253
0 252
1 251
1 250
1 249
1 248
1 247
0 246
0 245
0 244
0 243
0 242
0 241
0 240
1 239
0 238
0 237
0 236
0 235
0 234
0 233
0 232
0 231
0 230
0 229
0 228
0 227
0 226
0 225
0 224
0 223
0 222
0 221
0 220
0 219
0 218
0 217
0 216
0 215
0 214
0 213
0 212
0 211
0 210
0 29
0 28
0 27
0 26
0 25
0 24
1 23
0 22
0 21
1 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
0010 1111 0001 1111 0000 0001 0000 0000 0000 0000 0000 0000 0000 0000 0001 0010(2) =
(0 × 263 + 0 × 262 + 1 × 261 + 0 × 260 + 1 × 259 + 1 × 258 + 1 × 257 + 1 × 256 + 0 × 255 + 0 × 254 + 0 × 253 + 1 × 252 + 1 × 251 + 1 × 250 + 1 × 249 + 1 × 248 + 0 × 247 + 0 × 246 + 0 × 245 + 0 × 244 + 0 × 243 + 0 × 242 + 0 × 241 + 1 × 240 + 0 × 239 + 0 × 238 + 0 × 237 + 0 × 236 + 0 × 235 + 0 × 234 + 0 × 233 + 0 × 232 + 0 × 231 + 0 × 230 + 0 × 229 + 0 × 228 + 0 × 227 + 0 × 226 + 0 × 225 + 0 × 224 + 0 × 223 + 0 × 222 + 0 × 221 + 0 × 220 + 0 × 219 + 0 × 218 + 0 × 217 + 0 × 216 + 0 × 215 + 0 × 214 + 0 × 213 + 0 × 212 + 0 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 0 × 26 + 0 × 25 + 1 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 0 × 20)(10) =
(0 + 0 + 2 305 843 009 213 693 952 + 0 + 576 460 752 303 423 488 + 288 230 376 151 711 744 + 144 115 188 075 855 872 + 72 057 594 037 927 936 + 0 + 0 + 0 + 4 503 599 627 370 496 + 2 251 799 813 685 248 + 1 125 899 906 842 624 + 562 949 953 421 312 + 281 474 976 710 656 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 1 099 511 627 776 + 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 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 16 + 0 + 0 + 2 + 0)(10) =
(2 305 843 009 213 693 952 + 576 460 752 303 423 488 + 288 230 376 151 711 744 + 144 115 188 075 855 872 + 72 057 594 037 927 936 + 4 503 599 627 370 496 + 2 251 799 813 685 248 + 1 125 899 906 842 624 + 562 949 953 421 312 + 281 474 976 710 656 + 1 099 511 627 776 + 16 + 2)(10) =
3 395 433 743 572 271 122(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0010 1111 0001 1111 0000 0001 0000 0000 0000 0000 0000 0000 0000 0000 0001 0010(2) = 3 395 433 743 572 271 122(10)
The signed binary number in one's complement representation 0010 1111 0001 1111 0000 0001 0000 0000 0000 0000 0000 0000 0000 0000 0001 0010(2) converted and written as an integer in decimal system (base ten):
0010 1111 0001 1111 0000 0001 0000 0000 0000 0000 0000 0000 0000 0000 0001 0010(2) = 3 395 433 743 572 271 122(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.