How to convert decimal to binary

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:

  1. Get the highest power of 2 that is less than the decimal number x:

    max(2n) < x, (n = 1,2,3,...)

  2. The high binary digit is equal 1:

    dn = 1

  3. Calculate the difference Δ of the number x and he power of 2, 2n:

    Δ = x - 2n

  4. Repeat step #1 with the difference until the result is 0:

    x = Δ

Example

Convert x=13 to binary.

Solution

n=3, 23=8 < 13

n=4, 24=16 > 13

So

n = 3

d3 = 1

Δ = 13 - 23 = 5

n = 2, x = Δ = 5

d2 = 1

Δ = 5 - 22 = 1

n = 1, x = Δ = 1

d2 = 0

n = 0, x = Δ = 1

d0 = 1

Δ = 1 - 1 = 0

(d3d2d1d0) = 1101

So 13 in decimal is equal to 1101 in binary:

x = 1310 = 11012

 

How to convert binary to decimal ►

 


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