2. Multiply each bit by its corresponding power of 2 and add all the terms up.
101 0101 0111 1101(2) =
(1 × 214 + 0 × 213 + 1 × 212 + 0 × 211 + 1 × 210 + 0 × 29 + 1 × 28 + 0 × 27 + 1 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20)(10) =
(16 384 + 0 + 4 096 + 0 + 1 024 + 0 + 256 + 0 + 64 + 32 + 16 + 8 + 4 + 0 + 1)(10) =
(16 384 + 4 096 + 1 024 + 256 + 64 + 32 + 16 + 8 + 4 + 1)(10) =
21 885(10)
The number 101 0101 0111 1101(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 0101 0111 1101(2) = 21 885(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.