1. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
223
1 222
0 221
0 220
1 219
0 218
1 217
1 216
1 215
1 214
0 213
0 212
0 211
0 210
0 29
0 28
0 27
0 26
0 25
0 24
0 23
0 22
1 21
0 20
0
2. Multiply each bit by its corresponding power of 2 and add all the terms up:
1001 0111 1000 0000 0000 0100(2) =
(1 × 223 + 0 × 222 + 0 × 221 + 1 × 220 + 0 × 219 + 1 × 218 + 1 × 217 + 1 × 216 + 1 × 215 + 0 × 214 + 0 × 213 + 0 × 212 + 0 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 0 × 26 + 0 × 25 + 0 × 24 + 0 × 23 + 1 × 22 + 0 × 21 + 0 × 20)(10) =
(8 388 608 + 0 + 0 + 1 048 576 + 0 + 262 144 + 131 072 + 65 536 + 32 768 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 4 + 0 + 0)(10) =
(8 388 608 + 1 048 576 + 262 144 + 131 072 + 65 536 + 32 768 + 4)(10) =
9 928 708(10)
Conclusion: