Decimal to Binary converter

10
Binary number:
2
Binary signed 8-bit:
2
Binary signed 16-bit:
2
Binary signed 32-bit:
2
Hex number:
16

Binary to Decimal conversion ►

How to convert decimal to binary

To convert decimal number x to binary number:

  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

Decimal to binary conversion table

Decimal Binary
0 0
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000
9 1001
10 1010
11 1011
12 1100
13 1101
14 1110
15 1111
16 10000
17 10001
18 10010
19 10011
20 10100
21 10101
22 10110
23 10111
24 11000
25 11001
26 11010
27 11011
28 11100
29 11101
30 11110
31 11111
32 100000
64 1000000
128 10000000
256 100000000

 


See also

Write how to improve this page