2. Multiply each bit by its corresponding power of 2 and add all the terms up.
101 0000 0111 0000 0111 0001 1111 1111 1011(2) =
(1 × 234 + 0 × 233 + 1 × 232 + 0 × 231 + 0 × 230 + 0 × 229 + 0 × 228 + 0 × 227 + 1 × 226 + 1 × 225 + 1 × 224 + 0 × 223 + 0 × 222 + 0 × 221 + 0 × 220 + 0 × 219 + 1 × 218 + 1 × 217 + 1 × 216 + 0 × 215 + 0 × 214 + 0 × 213 + 1 × 212 + 1 × 211 + 1 × 210 + 1 × 29 + 1 × 28 + 1 × 27 + 1 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 0 × 22 + 1 × 21 + 1 × 20)(10) =
(17 179 869 184 + 0 + 4 294 967 296 + 0 + 0 + 0 + 0 + 0 + 67 108 864 + 33 554 432 + 16 777 216 + 0 + 0 + 0 + 0 + 0 + 262 144 + 131 072 + 65 536 + 0 + 0 + 0 + 4 096 + 2 048 + 1 024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 0 + 2 + 1)(10) =
(17 179 869 184 + 4 294 967 296 + 67 108 864 + 33 554 432 + 16 777 216 + 262 144 + 131 072 + 65 536 + 4 096 + 2 048 + 1 024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 2 + 1)(10) =
21 592 743 931(10)
The number 101 0000 0111 0000 0111 0001 1111 1111 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 0000 0111 0000 0111 0001 1111 1111 1011(2) = 21 592 743 931(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.