Conversion From Binary To Decimal Numbers (Expansion Method)

The expansion and place value method could be employed to do this type of conversion. This method could equally be used to convert from any other base number such as base 4, base 8, etc to decimal.

We use the expansion method to convert from binary back to decimal. In doing this, you have to expand the old number base.

Convert 101₂ to decimal

Answer – 101₂ =5₁₀

Remember: that any number raised to the power 0 is 1, Except 0

e.g 100⁰ = 1

Convert 10111₂ to decimal

Answer – 10111₂ = 23₁₀

Convert 00101 to decimal

Answer – 00101₂ = 5₁₀

The first 0 at the beginning of any number has no effect on the actual number (i.e 00101 is the same as 101)

Class Work:

Convert the following numbers from binary to decimal.

(a) 10100₂  (b) 10000₂ (c) 11001₂

Therefore, 10100₂ = 24₁₀