2. Multiply each bit by its corresponding power of 2 and add all the terms up.
101 1111 1100 1011 0000 0001 1111 1111 0000 1011 1000 0100 1011(2) =
(1 × 250 + 0 × 249 + 1 × 248 + 1 × 247 + 1 × 246 + 1 × 245 + 1 × 244 + 1 × 243 + 1 × 242 + 0 × 241 + 0 × 240 + 1 × 239 + 0 × 238 + 1 × 237 + 1 × 236 + 0 × 235 + 0 × 234 + 0 × 233 + 0 × 232 + 0 × 231 + 0 × 230 + 0 × 229 + 1 × 228 + 1 × 227 + 1 × 226 + 1 × 225 + 1 × 224 + 1 × 223 + 1 × 222 + 1 × 221 + 1 × 220 + 0 × 219 + 0 × 218 + 0 × 217 + 0 × 216 + 1 × 215 + 0 × 214 + 1 × 213 + 1 × 212 + 1 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 1 × 26 + 0 × 25 + 0 × 24 + 1 × 23 + 0 × 22 + 1 × 21 + 1 × 20)(10) =
(1 125 899 906 842 624 + 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 + 4 398 046 511 104 + 0 + 0 + 549 755 813 888 + 0 + 137 438 953 472 + 68 719 476 736 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 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 + 0 + 0 + 0 + 0 + 32 768 + 0 + 8 192 + 4 096 + 2 048 + 0 + 0 + 0 + 0 + 64 + 0 + 0 + 8 + 0 + 2 + 1)(10) =
(1 125 899 906 842 624 + 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 + 549 755 813 888 + 137 438 953 472 + 68 719 476 736 + 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 + 32 768 + 8 192 + 4 096 + 2 048 + 64 + 8 + 2 + 1)(10) =
1 685 208 263 866 443(10)
The number 101 1111 1100 1011 0000 0001 1111 1111 0000 1011 1000 0100 1011(2) converted from an unsigned binary (in base 2) and written as a positive integer (with no sign) in decimal system (in base ten):
101 1111 1100 1011 0000 0001 1111 1111 0000 1011 1000 0100 1011(2) = 1 685 208 263 866 443(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.