How to convert from decimal to binary :

Sometimes we need to convert numbers from decimal to binary. Here is how to do the same.

Divide the decimal number by 2 until quotient remains 0 and write the remainder each time you divide. How you will do this as shown below.

Note: each time you divide the decimal number by 2 then remainder will be always either 0 or 1 because we are dividing a decimal number by 2. There is no chance to remain other than 0 or 1 as a remainder.

Example: Suppose decimal number is (13)₁₀ and we would like to convert this (13)₁₀ into binary number.

2	13
2	6	1
2	3	0
2	1	1
	0	1

In above example first of all 13 is divided by 2 so quotient will be 6 and remainder will be 1. Again divide remaining quotient 6 by 2 so quotient is now 3 and remainder is 0. Now divide this quotient 3 by 2 so quotient will be 1 and remainder is 1 too. At the last quotient 1 is divided by 2 but 1 is not divided by 2 so quotient will be 0 and remainder will be 1 and it is finished. It always happen when quotient will remain 1 and it is not divided by 2 so quotient will be 0 and remainder will be 1.

After completion of this process write down the remainders from bottom to up. In above example (1101)₂. So binary number of 13 is (1101)₂.

Here is a list of decimal and its binary equivalent.

Decimal	Binary
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001
10	1010
11	1011
12	1100
13	1101
14	1110
15	1111

Another Example of Decimal to Binary conversion

Converting Decimal number 25 to its binary equivalent:

2	25
2	12	1
2	6	0
2	3	0
2	1	1
2	0	1

So writing remainders from bottom to up is (11001)₂. Binary equivalent of 25 is (11001)₂.