How is a binary number converted to a decimal number?

Answer 1

This is done in the same manner of converting a number in any non-decimal base (not base 10) to a decimal (base 10) number:

In each base system, the place value columns are the base times bigger than the column to its right.

The column before the base-point is the units or ones column. The next column left is the 1 × base = base column, the next column left is the base × base = base² column and so on.

To convert the number, sum each each digit of the base multiplied by its place value column.

For base 2, the place value columns (left from just left of the binary-point) are 1, 2, 2² = 4, 2³ = 8, 16, 32, ...

As a binary number only has 1s and 0s, converting a binary number to decimal is simply adding together the value of the place value columns that have a 1.

eg 101101₂ = 32 × 1 + 16 × 0 + 8 × 1 + 4 × 1 + 2 × 0 + 1 × 1 = 32 + 8 + 4 + 1 = 45