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Decimal to Binary Converter

Convert decimal numbers to binary (base 2) instantly. Visual bit grouping for easy reading.

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Binary to Decimal Converter

How to Convert Decimal to Binary

Repeatedly divide by 2 and record the remainders:

  1. Divide the decimal number by 2
  2. Record the remainder (0 or 1)
  3. Divide the quotient by 2 again
  4. Repeat until the quotient is 0
  5. Read the remainders in reverse order

Example: Convert 13 to binary:

  • 13 ÷ 2 = 6 remainder 1
  • 6 ÷ 2 = 3 remainder 0
  • 3 ÷ 2 = 1 remainder 1
  • 1 ÷ 2 = 0 remainder 1
  • Result: 1101 (reading remainders in reverse)

Code Examples

const decimal = 10;
const binary = decimal.toString(2); // "1010"
const padded = decimal.toString(2).padStart(8, '0'); // "00001010"

Frequently Asked Questions

How do I convert decimal to binary?

Divide the decimal number by 2 repeatedly, noting the remainders. Read the remainders in reverse order. For example, 10 ÷ 2 = 5r0, 5 ÷ 2 = 2r1, 2 ÷ 2 = 1r0, 1 ÷ 2 = 0r1, giving 1010.

How many bits do I need for a number?

The number of bits needed is ⌈log₂(n+1)⌉. Common sizes: 8 bits (0-255), 16 bits (0-65535), 32 bits (0-4.29B). Negative numbers require an extra sign bit.

What's the 0b prefix?

The 0b prefix indicates a binary number in languages like JavaScript, Python, and Rust. For example, 0b1010 equals decimal 10. It helps distinguish binary from decimal literals.

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