Binary Converter

Convert binary numbers to decimal or decimal numbers to binary quickly and accurately with our free online Binary Converter.

Convert Binary and Decimal Numbers

Enter a binary number using only 0 and 1.

What Is a Binary Number?

Binary is a number system that uses only two digits: 0 and 1. Unlike the decimal number system, which uses ten digits from 0 to 9, binary represents information using two possible states.

Binary is especially important in computing and digital electronics because computers process information using electrical states that can be represented as 0 and 1.

How Binary to Decimal Conversion Works

Each position in a binary number represents a power of 2. Starting from the right, the positions represent 20, 21, 22, 23, and so on.

For example, the binary number 1011 can be converted to decimal as follows:

Binary Digit Power of 2 Value
1 23 8
0 22 0
1 21 2
1 20 1

Therefore: 8 + 0 + 2 + 1 = 11. So, binary 1011 equals decimal 11.

How Decimal to Binary Conversion Works

To convert a positive decimal whole number to binary, the number can be repeatedly divided by 2. The remainders are then read from bottom to top to produce the binary number.

For example, decimal 13 is represented as binary 1101.

Calculation 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 gives 1101.

Common Binary and Decimal Examples

Binary Decimal
0 0
1 1
10 2
11 3
100 4
101 5
1010 10
1101 13
1111 15
10000 16

Where Binary Numbers Are Used

  • Computer systems and processors
  • Programming and software development
  • Digital electronics
  • Networking and data communication
  • Computer science and information technology
  • Digital storage and data representation

Frequently Asked Questions

What is binary?

Binary is a base-2 number system that uses only the digits 0 and 1.

What is 1010 in decimal?

Binary 1010 is equal to decimal 10.

What is 10 in binary?

Decimal 10 is equal to binary 1010.

Can this converter handle large numbers?

The converter is designed for normal whole-number conversions that can be safely represented by JavaScript. The calculator validates the input before performing the conversion.

Is this Binary Converter free?

Yes. CalclyWorld's Binary Converter is free to use and works directly in your browser without requiring an account.