Understanding Number Systems
A number system is a mathematical way to represent numbers. In computing and digital electronics, different bases are used for different purposes. Our calculator supports the four most common number systems:
Decimal (Base-10)
The standard number system used by humans in everyday life. It uses 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Binary (Base-2)
The fundamental language of computers. It uses only two digits: 0 and 1. Each digit is called a "bit" (binary digit). For example, the decimal number 13 is represented as 1101 in binary.
Octal (Base-8)
Uses 8 digits: 0 through 7. It was historically used in computing because three binary digits (bits) can be exactly represented by one octal digit.
Hexadecimal (Base-16)
Widely used in modern computing, especially for representing memory addresses and color codes (like HTML/CSS colors). It uses 16 symbols: 0-9 and A-F (where A=10, B=11, C=12, D=13, E=14, F=15). Four binary digits (a nibble) map perfectly to one hexadecimal digit.
How to Convert Binary to Decimal
To convert a binary number to decimal, you multiply each digit by 2 raised to the power of its position (starting from 0 on the far right) and add them together.
Example: Convert 1101 to decimal
- 1 × 2³ = 8
- 1 × 2² = 4
- 0 × 2¹ = 0
- 1 × 2⁰ = 1
- Total: 8 + 4 + 0 + 1 = 13
Our calculator shows these exact steps dynamically for any number you enter! Just type a number and expand the "How it works" section.