1. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
231
1 230
0 229
0 228
1 227
1 226
1 225
1 224
0 223
0 222
0 221
0 220
0 219
1 218
1 217
1 216
1 215
0 214
1 213
0 212
1 211
1 210
0 29
1 28
0 27
1 26
1 25
0 24
0 23
1 22
0 21
1 20
0
2. Multiply each bit by its corresponding power of 2 and add all the terms up:
1001 1110 0000 1111 0101 1010 1100 1010(2) =
(1 × 231 + 0 × 230 + 0 × 229 + 1 × 228 + 1 × 227 + 1 × 226 + 1 × 225 + 0 × 224 + 0 × 223 + 0 × 222 + 0 × 221 + 0 × 220 + 1 × 219 + 1 × 218 + 1 × 217 + 1 × 216 + 0 × 215 + 1 × 214 + 0 × 213 + 1 × 212 + 1 × 211 + 0 × 210 + 1 × 29 + 0 × 28 + 1 × 27 + 1 × 26 + 0 × 25 + 0 × 24 + 1 × 23 + 0 × 22 + 1 × 21 + 0 × 20)(10) =
(2 147 483 648 + 0 + 0 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 0 + 0 + 0 + 0 + 0 + 524 288 + 262 144 + 131 072 + 65 536 + 0 + 16 384 + 0 + 4 096 + 2 048 + 0 + 512 + 0 + 128 + 64 + 0 + 0 + 8 + 0 + 2 + 0)(10) =
(2 147 483 648 + 268 435 456 + 134 217 728 + 67 108 864 + 33 554 432 + 524 288 + 262 144 + 131 072 + 65 536 + 16 384 + 4 096 + 2 048 + 512 + 128 + 64 + 8 + 2)(10) =
2 651 806 410(10)