A binary to decimal converter is a tool that transforms binary numbers into their decimal equivalents. Each binary number is interpreted either as an unsigned number or as a signed number using two's complement representation.

How It Works

1. The input binary string is validated to ensure it contains only 0s and 1s (spaces are allowed for readability).
2. The user can choose between unsigned and signed (two's complement) interpretation.
3. For unsigned interpretation, each bit's value is calculated based on its position (2^position) and summed up.
4. For signed interpretation (two's complement), if the leftmost bit is 1, the number is negative. The two's complement conversion is applied to determine the magnitude.
5. The resulting decimal value is displayed.

Common Uses

• Computer Science Education:Understanding how binary numbers are interpreted as decimal values in computers.
• Digital Electronics:Converting binary signals from hardware into human-readable decimal values.
• Programming:Interpreting binary data read from files or network sockets as decimal numbers.
• Data Analysis:Converting binary-encoded data into decimal format for analysis.
• Cryptography:Converting binary-encoded keys or values into decimal for cryptographic calculations.

Binary System Basics

The binary system uses only two digits, 0 and 1, to represent numbers. Each digit in a binary number is called a bit. Binary numbers can be used to represent both positive and negative numbers using different methods, such as two's complement for negative numbers.