Binary ⇄ Decimal
Convert between binary and decimal numbers in both directions. Supports signed integers and shows the step-by-step positional value breakdown for each conversion.
How to use the binary ⇄ decimal
Enter a binary number; the decimal value computes instantly.
Formula & explanation
Each binary digit represents a power of 2. 1101 = 8+4+0+1 = 13.
Examples
11111111 (binary) = 255. 10000000 = 128.
Frequently asked questions
- How do I convert binary to decimal?
- Multiply each binary digit by its corresponding power of 2 (starting at 2⁰ on the right) and add the results. For example, 1101 = 8 + 4 + 0 + 1 = 13.
- What is binary used for?
- Binary (base-2) is the native language of computers. Every piece of data — text, images, programs — is ultimately stored and processed as sequences of 0s and 1s.
- How many decimal values can 8 binary digits (1 byte) represent?
- 8 bits can represent 256 values (0–255), since 2⁸ = 256.
- Why does binary only use 0 and 1?
- Electronic circuits can reliably distinguish two voltage states (on/off), making base-2 the natural fit for digital hardware.
Related number & code tools
- Hex ⇄ DecimalConvert between hexadecimal and decimal numbers. Supports uppercase and lowercase hex input — useful for color codes, memory addresses, and network protocols.
- Binary ⇄ HexConvert between binary and hexadecimal notation. Handles any length input and groups binary output into nibbles (4-bit groups) for readability.
- Octal ⇄ DecimalConvert between octal (base 8) and decimal (base 10). Useful for Unix file permissions, legacy computing, and programming exercises involving number systems.
- Number Base ConverterConvert any number between any two bases from 2 (binary) to 36. Enter the source base, target base, and number — ideal for computer science and custom encoding schemes.
- BCD ConverterConvert decimal numbers to Binary-Coded Decimal (BCD) and back. Shows the 4-bit group encoding for each decimal digit — useful for electronics and embedded systems.
- ASCII ConverterConvert text to ASCII character codes and ASCII codes back to text. Shows decimal, hexadecimal, and binary representations for each character simultaneously.