# Decimal to Binary

## Calculator

The following calculator will help you to convert a Decimal number to a Binary number.

## Examples

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).

NumberCalculationQuotientRemainder
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.

## Examples

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).

NumberCalculationQuotientRemainder
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'.

## Examples

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.

NumberCalculationQuotientRemainder
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.

NumberCalculationResultInteger
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)