Decimal to Binary converter

Enter decimal number:
	10
Convert Reset Swap
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:

   d_n = 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

• Binary to Decimal converter
• Decimal to Hex converter
• Decimal to Octal converter
• Decimal to Fraction converter
• Decimal to Percent converter
• ASCII text to binary converter
• Numeral systems
• Conversion