2. Multiply each bit by its corresponding power of 2 and add all the terms up.
10 0000 1000 1011 1101 1110 1010 1001 0101 0100 0001 1110 0000 0111(2) =
(1 × 253 + 0 × 252 + 0 × 251 + 0 × 250 + 0 × 249 + 0 × 248 + 1 × 247 + 0 × 246 + 0 × 245 + 0 × 244 + 1 × 243 + 0 × 242 + 1 × 241 + 1 × 240 + 1 × 239 + 1 × 238 + 0 × 237 + 1 × 236 + 1 × 235 + 1 × 234 + 1 × 233 + 0 × 232 + 1 × 231 + 0 × 230 + 1 × 229 + 0 × 228 + 1 × 227 + 0 × 226 + 0 × 225 + 1 × 224 + 0 × 223 + 1 × 222 + 0 × 221 + 1 × 220 + 0 × 219 + 1 × 218 + 0 × 217 + 0 × 216 + 0 × 215 + 0 × 214 + 0 × 213 + 1 × 212 + 1 × 211 + 1 × 210 + 1 × 29 + 0 × 28 + 0 × 27 + 0 × 26 + 0 × 25 + 0 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 1 × 20)(10) =
(9 007 199 254 740 992 + 0 + 0 + 0 + 0 + 0 + 140 737 488 355 328 + 0 + 0 + 0 + 8 796 093 022 208 + 0 + 2 199 023 255 552 + 1 099 511 627 776 + 549 755 813 888 + 274 877 906 944 + 0 + 68 719 476 736 + 34 359 738 368 + 17 179 869 184 + 8 589 934 592 + 0 + 2 147 483 648 + 0 + 536 870 912 + 0 + 134 217 728 + 0 + 0 + 16 777 216 + 0 + 4 194 304 + 0 + 1 048 576 + 0 + 262 144 + 0 + 0 + 0 + 0 + 0 + 4 096 + 2 048 + 1 024 + 512 + 0 + 0 + 0 + 0 + 0 + 0 + 4 + 2 + 1)(10) =
(9 007 199 254 740 992 + 140 737 488 355 328 + 8 796 093 022 208 + 2 199 023 255 552 + 1 099 511 627 776 + 549 755 813 888 + 274 877 906 944 + 68 719 476 736 + 34 359 738 368 + 17 179 869 184 + 8 589 934 592 + 2 147 483 648 + 536 870 912 + 134 217 728 + 16 777 216 + 4 194 304 + 1 048 576 + 262 144 + 4 096 + 2 048 + 1 024 + 512 + 4 + 2 + 1)(10) =
9 160 987 694 603 783(10)
The number 10 0000 1000 1011 1101 1110 1010 1001 0101 0100 0001 1110 0000 0111(2) converted from an unsigned binary (in base 2) and written as a positive integer (with no sign) in decimal system (in base ten):
10 0000 1000 1011 1101 1110 1010 1001 0101 0100 0001 1110 0000 0111(2) = 9 160 987 694 603 783(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.