Decimal to Binary Converter

Convert decimal (base-10) numbers to binary (base-2) representation. Perfect for understanding computer number systems and programming.

Input (Decimal)
Enter a decimal number
Output (Binary)
Binary representation

What is Decimal to Binary Conversion?

Decimal to binary conversion transforms base-10 numbers (our everyday counting system) into base-2 numbers (the binary system used by computers).

Why is Binary Important?

Binary is the fundamental language of computers. All data in computers is ultimately stored and processed as sequences of 0s and 1s.

Common Use Cases:

  • Understanding computer architecture
  • Low-level programming and bit manipulation
  • Network addressing and subnet masks
  • Digital electronics and circuit design

How Does It Work?

Decimal to binary conversion involves repeatedly dividing the decimal number by 2 and recording the remainders in reverse order.

Example:

  • Decimal 42 becomes Binary 101010
  • Decimal 255 becomes Binary 11111111
  • Decimal 10 becomes Binary 1010

Understanding Binary

Each position in a binary number represents a power of 2:

  • Position 0 (rightmost): 2^0 = 1
  • Position 1: 2^1 = 2
  • Position 2: 2^2 = 4
  • Position 3: 2^3 = 8
  • And so on...

So 101010 in binary equals: 32 + 8 + 2 = 42 in decimal.