Decimal To Binary Converter
Enter the decimal value to convert to binary or Binary to Decimal.
Decimal:
The decimal (Base-10) number system uses digits 0-9 and is the most commonly used number system in everyday life.
Binary:
The binary (Base-2) number system uses only 0 and 1. It is the foundation of all digital computing and electronic circuits.
How to Convert Decimal to Binary — Formula:
Repeatedly divide the decimal number by 2 and record the remainders. Read remainders from bottom to top.
Example: 13 ÷ 2 = 6 R1, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1 → Binary: 1101.
Technical Details:
Common decimal-to-binary conversions: 0=0, 1=1, 2=10, 4=100, 8=1000, 16=10000, 32=100000, 64=1000000, 128=10000000, 255=11111111, 256=100000000.
Decimal To Binary Converter:
Convert any decimal number to its binary equivalent instantly. Supports both integer and fractional numbers with detailed conversion steps.
Binary to Decimal: How Each Bit Has a Value
128 + 32 + 16 + 4 + 2 = 182
How to Convert Decimal to Binary
- Divide the decimal number by 2
- Write down the remainder (0 or 1)
- Divide the quotient by 2 again
- Repeat until the quotient is 0
- Read the remainders from bottom to top
Example
Convert decimal 156 to binary:
156 ÷ 2 = 78 remainder 0
78 ÷ 2 = 39 remainder 0
39 ÷ 2 = 19 remainder 1
19 ÷ 2 = 9 remainder 1
9 ÷ 2 = 4 remainder 1
4 ÷ 2 = 2 remainder 0
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Read bottom to top: 10011100₂
Frequently Asked Questions
How do I convert Decimal to Binary?
Repeatedly divide the decimal number by 2 and record the remainders. Read remainders from bottom to top.
What is the Decimal number system?
The decimal (Base-10) number system uses digits 0-9 and is the most commonly used number system in everyday life.
What is the Binary number system?
The binary (Base-2) number system uses only 0 and 1. It is the foundation of all digital computing and electronic circuits.
Where is Decimal to Binary conversion used?
Common decimal-to-binary conversions: 0=0, 1=1, 2=10, 4=100, 8=1000, 16=10000, 32=100000, 64=1000000, 128=10000000, 255=11111111, 256=100000000.
Can I convert large decimal numbers?
Yes. This converter handles numbers of any practical size. For very large numbers, the conversion is performed using arbitrary-precision arithmetic to ensure accuracy.