Binary to Decimal Converter
A comprehensive binary number converter that transforms binary numbers to decimal, displays two's complement representation, and provides hexadecimal conversion. Perfect for programmers, students, and digital electronics enthusiasts.
Binary to Decimal converter
About Binary Numbers
Binary numbers are the foundation of digital computing, using only two digits (0 and 1) to represent values. This number system is fundamental to how computers store and process data. The two's complement representation is particularly important as it allows computers to handle negative numbers efficiently. Converting between binary and decimal systems is a crucial skill for anyone working with computers, digital electronics, or low-level programming.
Frequently Asked Questions
What is a binary number?
A binary number is a number expressed using only two digits: 0 and 1. Each digit in a binary number represents a power of 2, making it the foundation of digital computing systems.
What is Two's Complement?
Two's complement is a method used to represent negative numbers in binary. It's calculated by inverting all the bits of a binary number and adding 1 to the result. This representation allows computers to perform arithmetic operations on both positive and negative numbers.
Why convert binary to decimal?
While computers work with binary numbers internally, humans find it easier to work with decimal numbers. Converting between the two systems is essential for debugging, programming, and understanding how computers process data.
What is hexadecimal (hex)?
Hexadecimal is a base-16 number system that uses digits 0-9 and letters A-F. It's commonly used in computing as a more concise way to represent binary numbers, where each hex digit represents exactly 4 binary digits.
How accurate is this converter?
This converter provides precise conversions for binary numbers. However, due to JavaScript's number handling limitations, it's most reliable for binary numbers up to 52 bits in length. For longer numbers, consider using specialized mathematical libraries.
How It Works
Converting binary to decimal involves multiplying each digit by powers of 2:
- Start from the rightmost digit
- Multiply each digit by 2 raised to its position (starting from 0)
- Add up all the results
- The sum is your decimal number