How to convert decimal to binary

How to convert from decimal number to binary number.

How to convert base 10 to base 2.

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(2ⁿ) < x, (n = 1,2,3,...)
The high binary digit is equal 1:
d_n = 1
Calculate the difference Δ of the number x and he power of 2, 2ⁿ:
Δ = x - 2ⁿ
Repeat step #1 with the difference until the result is 0:
x = Δ

Convert x=13 to binary.

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