# Decimal to Binary Converter

You are Here:

## 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
2222 % 2110
1111 % 251
55 % 221
22 % 210
11 % 201

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
7575 % 2371
3737 % 2181
1818 % 290
99 % 241
44 % 220
22 % 210
11 % 201

-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
1515 % 271
77 % 231
33 % 211
11 % 201

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
0.1250.125 × 20.2500
0.2500.250 × 20.5000
0.5000.500 × 211

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)