Decimal to Binary

In this example, we will convert the positive integer decimal number to a binary number.

The following table provides the detail explanation of how to convert decimal (22) into binary number (10110).

Number	Calculation	Quotient	Remainder
22	22 % 2	11	0
11	11 % 2	5	1
5	5 % 2	2	1
2	2 % 2	1	0
1	1 % 2	0	1

22 (decimal) = 10110 (binary)

Note: Read the remainder from bottom to top.

In this example, we will convert the negative integer decimal number to a binary number.

The following table provides the detail explanation of how to convert decimal (-75) into binary number (-1001011).

Number	Calculation	Quotient	Remainder
75	75 % 2	37	1
37	37 % 2	18	1
18	18 % 2	9	0
9	9 % 2	4	1
4	4 % 2	2	0
2	2 % 2	1	0
1	1 % 2	0	1

-75 (decimal) = -1001011 (binary)

Note: Read the remainder from bottom to top.

Explanation: For negative integer decimal to binary number, proceed the steps as same as positive integer decimal to binary number and finally multiply the output by '-1'.

In this example, we will convert the fractional decimal number (15.125) to a binary number (1111.001).

Here, we have to split the fractional decimal number into two parts.

1. Integer part - 15
2. Fraction part - 0.125

Now, convert the Integer part of the given decimal number (15) into a binary number.

Number	Calculation	Quotient	Remainder
15	15 % 2	7	1
7	7 % 2	3	1
3	3 % 2	1	1
1	1 % 2	0	1

15 (decimal) = 1111 (binary)

Note: Read the remainder from bottom to top.

Now, convert the Fraction part of the given decimal number (0.125) into a binary number.

Number	Calculation	Result	Integer
0.125	0.125 × 2	0.250	0
0.250	0.250 × 2	0.500	0
0.500	0.500 × 2	1	1

0.125 (decimal) = 001 (binary)

Note: Read the Integer from top to bottom.

Explanation: Here, you have to stop the table when no more fractional part is available in 'Result' column of table 2. 'Integer' column in table 2 occurs from the integer part of 'Result' column of table 2.

Now, join both the result

15.125 (decimal) = 1111.001 (binary)