Decimal to Hexadecimal Converter

Convert a whole decimal number to hexadecimal.

How the Math Works

To convert a decimal number to hexadecimal, binary, and octal, we use repeated division by the target base (16 for hex, 2 for binary, 8 for octal). For each base, divide the decimal number by the base, record the remainder, then divide the quotient by the base again. Repeat until the quotient is zero. The remainders, read in reverse order, form the converted number. For example, converting 255 to hex: 255 ÷ 16 = 15 remainder 15 (F), then 15 ÷ 16 = 0 remainder 15 (F), resulting in FF. This method works similarly for binary (base 2) and octal (base 8).

Practical Applications

This conversion is essential in computer science and programming for tasks like memory addressing, where hexadecimal is used to represent bytes compactly (e.g., 0x7C9B for memory addresses). It's also critical in networking for IP address subnetting and in electronics for digital circuit design, where binary and octal simplify hardware logic. Developers use these conversions when debugging code, working with bitwise operations, or translating color codes (e.g., #FF0000 for red in web design requires hex knowledge).

Day-to-Day Use

In everyday technology use, hexadecimal simplifies representing binary data in a human-friendly format, such as in computer file permissions (e.g., 777 in octal), USB device identifiers, or QR code encoding. Understanding these conversions helps troubleshoot issues with digital devices, interpret system logs, or engage with modern technologies like cryptocurrency (e.g., hex hashes for transactions). Even in gaming, hexadecimal is used in modding or understanding game file structures, making it a foundational skill for tech-savvy individuals.

Worked example

255 → FF.

FAQ