Binary to Decimal Converter

Understanding Hexadecimal

Hexadecimal (often called "hex") is a base-16 number system that uses sixteen digits: 0-9 and A-F (where A=10, B=11, C=12, D=13, E=14, F=15). It's widely used in computing because it provides a compact, human-readable way to represent binary data.

Hexadecimal is a positional number system, just like decimal. But instead of each position representing a power of 10 (1, 10, 100, 1000...), each position represents a power of 16 (1, 16, 256, 4096...). The rightmost position is 16⁰ (1), next is 16¹ (16), then 16² (256), then 16³ (4096), and so on.

Hexadecimal position values: ... 4096 256 16 1

To convert hexadecimal to decimal, you multiply each digit by its position value and add up the results. For digits A-F, you first convert them to their decimal equivalents (10-15).

Step-by-Step Conversion Method

Here's exactly how to convert hexadecimal to decimal using the positional value method:

1. Write down the hexadecimal number - For example, 2A7
2. Convert any letters to numbers - A=10, B=11, C=12, D=13, E=14, F=15
3. Number the positions from right to left - Start with 0 on the right
4. Multiply each digit by 16 raised to its position - Use 16⁰, 16¹, 16², etc.
5. Add up all the results - The sum is the decimal equivalent

Our converter shows you these steps for any hexadecimal number you enter, including the conversion of letters A-F to numbers 10-15.

Hexadecimal Digit Values

Here's the complete hexadecimal digit system:

Notice that each hexadecimal digit corresponds to exactly four binary digits. This makes hex-to-binary and binary-to-hex conversions very straightforward.

Common Hexadecimal to Decimal Conversions

Here are important hexadecimal numbers and their decimal equivalents:

Try converting these hexadecimal numbers using our converter to practice!

Hexadecimal in Web Colors

One of the most common uses of hexadecimal is in web color codes. Colors on the web are specified using a # followed by six hexadecimal digits representing red, green, and blue components:

Hexadecimal in Programming

Programmers use hexadecimal extensively because:

• Memory Addresses - Computer memory locations are shown in hexadecimal
• Debugging - Debuggers show data in hexadecimal (hex dumps)
• Bit Masks - Hex makes it easy to work with specific bits (each hex digit = 4 bits)
• Constants - Programmers use hex for constants (0xFF for 255)
• Assembly Language - Low-level programming uses hex extensively
• Error Codes - Some error messages use hexadecimal codes