Best uses
- Understand how computers represent decimal numbers.
- Check classwork, coding examples, or electronics values.
- Convert integers before using them in bit operations.
Number converters
Decimal to Binary Converter
Convert decimal numbers to binary online with divide-by-2 steps, examples, quality checks, FAQs, and common base conversion mistakes.
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Works on any device
10
2
Decimal to binary calcution steps:
How to convert a decimal number to the binary number?
To convert the whole-number part of a decimal value to binary, divide by 2 and read the remainders in reverse order. For the fractional part, multiply by 2 repeatedly and record each whole-number result until the fraction becomes 0 or reaches the precision you need. The example below shows the process:
Example of decimal to binary conversion:
(10.25)10 = (?)2
For 10:
| Divided by 2 | Quotient | Remainder | Flow |
|---|---|---|---|
| 10 / 2 | 5 | 0 | ↓ |
| 5 / 2 | 2 | 1 | ↓ |
| 2 / 2 | 1 | 0 | ↓ |
| 1 / 2 | 0 | 1 | ↓ |
For .25:
| Multiply by 2 | Result | Non-Fractional Part | Flow |
|---|---|---|---|
| .25 * 2 | 0.50 | 0 | ↓ |
| .50 * 2 | 1.00 | 1 | ↓ |
Result is = (1010.01)2
Why decimal to binary matters
Decimal numbers are easy for people to read, while binary is the base used in digital systems. Converting decimal to binary helps with programming lessons, bitwise operations, networking examples, computer architecture, and digital electronics problems.
How to check your result
- Each binary digit represents a power of 2.
- Reading from right to left, the places are 1, 2, 4, 8, 16, and so on.
- Add the values of the positions that contain 1 to get back the decimal number.
- For fractions, remember that some decimal fractions do not end cleanly in binary.
Decimal to binary conversion table:
| Decimal | Binary |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 8 | 1000 |
| 9 | 1001 |
| 10 | 1010 |
| 11 | 1011 |
| 12 | 1100 |
| 13 | 1101 |
| 14 | 1110 |
| 15 | 1111 |
Interpret negative values and fractions correctly
A leading minus sign describes a negative mathematical value; it is not a fixed-width computer encoding. Programming systems may store the same negative integer using two’s complement with a specified bit width, producing a different visible bit pattern. Use this page for ordinary base notation unless your task explicitly asks for an 8-bit, 16-bit, 32-bit, or 64-bit signed representation.
For a fractional decimal, repeatedly multiply the fractional part by 2 and record each whole-number digit in order. Some decimal fractions repeat indefinitely in binary, so a displayed answer may stop after a practical number of places. Convert the result back to decimal and compare within the required tolerance instead of expecting every fraction to terminate exactly.
Decimal to binary guide
To convert a decimal whole number to binary, divide by 2 and track the remainders. Read the remainders from bottom to top to get the binary value.
Quality checks
- Use only whole-number division for the integer part.
- Read remainders upward, not in the order they were created.
- For fractions, multiply the fractional part by 2 repeatedly.
Common mistakes
- Reading remainders from top to bottom.
- Stopping before the quotient reaches zero.
- Mixing decimal digits with binary output digits.
Quick answers
How do I convert 42 to binary?
Divide by 2 repeatedly and read the remainders upward. 42 becomes 101010.
Why does binary only use 0 and 1?
Binary is base 2, so each digit can only represent two possible values.