Decimal to Binary Converter
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).
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.
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).
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'.
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.
- Integer part - 15
- 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)Useful links
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