Number Base Converter

Convert a whole decimal number into the binary, hexadecimal and octal systems used in computing.

How the Math Works

The Number Base Converter uses the fundamental division-remainder method to transform decimal numbers into other bases. To convert a decimal number to binary (base-2), hexadecimal (base-16), or octal (base-8), you repeatedly divide the number by the target base and record the remainders. For example, converting 25 to binary: 25 ÷ 2 = 12 remainder 1, 12 ÷ 2 = 6 remainder 0, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1. Reading the remainders from bottom to top gives you 11001 in binary. The same process works for any base by simply changing the divisor.

Practical Applications

To use this converter for practical calculations, enter your decimal number into the input field and select the bases you want to convert to. The calculator instantly applies the division algorithm to show you the equivalent values. This is essential for computer science tasks where you need to work with binary for logic operations, hexadecimal for memory addresses and color codes, or octal for file permissions in Unix systems. You can also verify your manual calculations by converting known values and checking if the results match your expected outcomes.

Day-to-Day Use

Understanding number base conversions helps in everyday technology interactions. When debugging code, you might need to interpret memory dumps displayed in hexadecimal. Setting file permissions in Linux systems requires understanding octal notation (like 755 for read/write/execute). Many programming concepts become clearer when you can mentally convert between bases. Additionally, certain electronics and networking tasks use these number systems, making this knowledge valuable for troubleshooting devices or understanding how computers actually store and process information at the fundamental level.

Worked example

255 → binary 11111111, hex FF, octal 377.

FAQ