How to convert from decimal number to binary number.

How to convert base 10 to base 2.

### How to convert decimal to binary

In order to convert decimal number x to binary number:

For decimal number x:

- Get the highest power of 2 that is less than the decimal number x:
max(2

) <^{n}*x*, (*n*= 1,2,3,...) - The high binary digit is equal 1:
*d*= 1_{n} - Calculate the difference Δ of the number x and he power of 2, 2
^{n}:Δ =

*x*- 2^{n} - Repeat step #1 with the difference until the result is 0:
*x*= Δ

#### Example

Convert x=13 to binary.

#### Solution

*n*=3, 2^{3}=8 < 13

*n*=4, 2^{4}=16 > 13

So

*n *= 3

*d*_{3} = 1

Δ = 13 - 2^{3} = 5

*n *= 2, *x* = Δ = 5

*d*_{2} = 1

Δ = 5 - 2^{2} = 1

*n *= 1, *x* = Δ = 1

*d*_{2} = 0

*n *= 0, *x* = Δ = 1

*d*_{0} = 1

Δ = 1 - 1 = 0

(*d*_{3}*d*_{2}*d*_{1}*d*_{0}) = 1101

So 13 in decimal is equal to 1101 in binary:

*x* = 13_{10} = 1101_{2}

How to convert binary to decimal ►