2. Multiply each bit by its corresponding power of 2 and add all the terms up.
1 0000 0001 0000 0111 0111(2) =
(1 × 220 + 0 × 219 + 0 × 218 + 0 × 217 + 0 × 216 + 0 × 215 + 0 × 214 + 0 × 213 + 1 × 212 + 0 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 0 × 27 + 1 × 26 + 1 × 25 + 1 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 1 × 20)(10) =
(1 048 576 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 4 096 + 0 + 0 + 0 + 0 + 0 + 64 + 32 + 16 + 0 + 4 + 2 + 1)(10) =
(1 048 576 + 4 096 + 64 + 32 + 16 + 4 + 2 + 1)(10) =
1 052 791(10)
The number 1 0000 0001 0000 0111 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):
1 0000 0001 0000 0111 0111(2) = 1 052 791(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.