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Decimal to Binary Converter

Convert decimal numbers to binary

What is Decimal to Binary Conversion?

Decimal to binary conversion transforms our everyday base-10 numbers into the base-2 format computers use internally. It's a fundamental operation in computer science and essential for understanding how digital systems work.

Enter any positive integer, get its binary representation instantly. Great for learning, teaching, or quick reference during programming.

The Conversion Process

Think of decimal-to-binary conversion as asking: 'Which powers of 2 add up to this number?' For 13, we need 8+4+1, so we set bits at positions 3, 2, and 0: 1101.

The systematic method divides by 2 repeatedly, collecting remainders. It's the reverse of the multiplication method used for binary-to-decimal.

Why This Matters

Understanding binary helps with:

  • Bit manipulation in programming
  • Understanding memory and data sizes
  • Working with bitwise operators
  • Debugging low-level code
  • Computer architecture concepts

Frequently Asked Questions

How do I convert decimal to binary manually?

Repeatedly divide by 2, recording remainders. Read remainders bottom-to-top. For 10: 10÷2=5r0, 5÷2=2r1, 2÷2=1r0, 1÷2=0r1. Result: 1010.

Why is binary important for computers?

Computers use electrical signals that are either on or off, naturally representing 1 and 0. All data - text, images, programs - is ultimately stored and processed as binary.

What's the binary for common numbers?

5=101, 10=1010, 100=1100100, 255=11111111, 1000=1111101000. Powers of 2 are single 1s: 2=10, 4=100, 8=1000, 16=10000.

Decimal

Binary