1. Is this a positive or a negative number?
1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1001 1100 0110 1010 is the binary representation of a negative integer, on 64 bits (8 Bytes).
In a signed binary, the first bit (the leftmost) is reserved for the sign,
1 = negative, 0 = positive. This bit does not count when calculating the absolute value.
2. Construct the unsigned binary number.
Exclude the first bit (the leftmost), that is reserved for the sign:
1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1001 1100 0110 1010 = 111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1001 1100 0110 1010
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
262
1 261
1 260
1 259
1 258
1 257
1 256
1 255
1 254
1 253
1 252
1 251
1 250
1 249
1 248
1 247
1 246
1 245
1 244
1 243
1 242
1 241
1 240
1 239
1 238
1 237
1 236
1 235
1 234
1 233
1 232
1 231
1 230
1 229
1 228
1 227
1 226
1 225
1 224
1 223
1 222
1 221
1 220
1 219
1 218
1 217
1 216
1 215
1 214
0 213
0 212
1 211
1 210
1 29
0 28
0 27
0 26
1 25
1 24
0 23
1 22
0 21
1 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1001 1100 0110 1010(2) =
(1 × 262 + 1 × 261 + 1 × 260 + 1 × 259 + 1 × 258 + 1 × 257 + 1 × 256 + 1 × 255 + 1 × 254 + 1 × 253 + 1 × 252 + 1 × 251 + 1 × 250 + 1 × 249 + 1 × 248 + 1 × 247 + 1 × 246 + 1 × 245 + 1 × 244 + 1 × 243 + 1 × 242 + 1 × 241 + 1 × 240 + 1 × 239 + 1 × 238 + 1 × 237 + 1 × 236 + 1 × 235 + 1 × 234 + 1 × 233 + 1 × 232 + 1 × 231 + 1 × 230 + 1 × 229 + 1 × 228 + 1 × 227 + 1 × 226 + 1 × 225 + 1 × 224 + 1 × 223 + 1 × 222 + 1 × 221 + 1 × 220 + 1 × 219 + 1 × 218 + 1 × 217 + 1 × 216 + 1 × 215 + 0 × 214 + 0 × 213 + 1 × 212 + 1 × 211 + 1 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 1 × 26 + 1 × 25 + 0 × 24 + 1 × 23 + 0 × 22 + 1 × 21 + 0 × 20)(10) =
(4 611 686 018 427 387 904 + 2 305 843 009 213 693 952 + 1 152 921 504 606 846 976 + 576 460 752 303 423 488 + 288 230 376 151 711 744 + 144 115 188 075 855 872 + 72 057 594 037 927 936 + 36 028 797 018 963 968 + 18 014 398 509 481 984 + 9 007 199 254 740 992 + 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 + 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 + 4 398 046 511 104 + 2 199 023 255 552 + 1 099 511 627 776 + 549 755 813 888 + 274 877 906 944 + 137 438 953 472 + 68 719 476 736 + 34 359 738 368 + 17 179 869 184 + 8 589 934 592 + 4 294 967 296 + 2 147 483 648 + 1 073 741 824 + 536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 16 777 216 + 8 388 608 + 4 194 304 + 2 097 152 + 1 048 576 + 524 288 + 262 144 + 131 072 + 65 536 + 32 768 + 0 + 0 + 4 096 + 2 048 + 1 024 + 0 + 0 + 0 + 64 + 32 + 0 + 8 + 0 + 2 + 0)(10) =
(4 611 686 018 427 387 904 + 2 305 843 009 213 693 952 + 1 152 921 504 606 846 976 + 576 460 752 303 423 488 + 288 230 376 151 711 744 + 144 115 188 075 855 872 + 72 057 594 037 927 936 + 36 028 797 018 963 968 + 18 014 398 509 481 984 + 9 007 199 254 740 992 + 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 + 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 + 4 398 046 511 104 + 2 199 023 255 552 + 1 099 511 627 776 + 549 755 813 888 + 274 877 906 944 + 137 438 953 472 + 68 719 476 736 + 34 359 738 368 + 17 179 869 184 + 8 589 934 592 + 4 294 967 296 + 2 147 483 648 + 1 073 741 824 + 536 870 912 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 16 777 216 + 8 388 608 + 4 194 304 + 2 097 152 + 1 048 576 + 524 288 + 262 144 + 131 072 + 65 536 + 32 768 + 4 096 + 2 048 + 1 024 + 64 + 32 + 8 + 2)(10) =
9 223 372 036 854 750 314(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1001 1100 0110 1010(2) = -9 223 372 036 854 750 314(10)
The number 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1001 1100 0110 1010(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1001 1100 0110 1010(2) = -9 223 372 036 854 750 314(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.