Decimal to Binary Converter
Enter the decimal number you want to convert to binary.
Table of Contents
- How does decimal to binary conversion work?
- Decimal to binary conversion formula
- Conversion process
- Examples
- Decimal to binary conversion table
- Frequently Asked Questions
How does decimal to binary conversion work?
The decimal system is base 10 and the binary system is base 2. To convert a decimal number to binary, repeatedly divide the number by 2 and record the remainders. Then, read the remainders in reverse order (from bottom to top) to obtain the binary number.
Decimal to binary conversion formula
To convert a decimal number N to binary:
Where the coefficients bi (remainders) are 0 or 1, obtained by repeatedly dividing N by 2. The binary number is formed by reading the remainders from bottom to top.
Conversion process
- Divide the decimal number by 2 and note the remainder (0 or 1).
- Take the quotient obtained and repeat the division by 2 until you reach 0.
- Write the remainders in reverse order (from bottom to top) to obtain the binary number.
Examples
13₁₀ to binary| Division | Quotient | Remainder |
|---|---|---|
| 13 ÷ 2 | 6 | 1 |
| 6 ÷ 2 | 3 | 0 |
| 3 ÷ 2 | 1 | 1 |
| 1 ÷ 2 | 0 | 1 |
Reading the remainders from bottom to top: 1101₂.
Result: 13₁₀ = 1101₂.
45₁₀ to binary| Division | Quotient | Remainder |
|---|---|---|
| 45 ÷ 2 | 22 | 1 |
| 22 ÷ 2 | 11 | 0 |
| 11 ÷ 2 | 5 | 1 |
| 5 ÷ 2 | 2 | 1 |
| 2 ÷ 2 | 1 | 0 |
| 1 ÷ 2 | 0 | 1 |
Reading the remainders from bottom to top: 101101₂.
Result: 45₁₀ = 101101₂.
Decimal to binary conversion table
Quick reference values for small decimal numbers.
| Decimal | Binary |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 3 | 11 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
| 8 | 1000 |
| 9 | 1001 |
| 10 | 1010 |
| 16 | 10000 |
| 32 | 100000 |
| 64 | 1000000 |
| 128 | 10000000 |
| 256 | 100000000 |
| 512 | 1000000000 |
| 1024 | 10000000000 |
Frequently Asked Questions
How do you convert a decimal number to binary?
To convert a decimal number to binary, repeatedly divide the number by 2 and record the remainders. Finally, read the remainders in reverse order (from bottom to top) to obtain the binary number.
What is the binary representation of 25?
The decimal number 25 converted to binary is 11001₂.