Perform arithmetic in hexadecimal, and convert between hex, decimal, binary, and octal number systems.
This tool converts numbers between hexadecimal (base 16), decimal (base 10), and binary (base 2), and can perform arithmetic directly on hexadecimal values. Hexadecimal is widely used in computing and programming to represent binary data in a more compact, human-readable form.
Hexadecimal uses 16 symbols (0-9 and A-F, where A=10 through F=15). Each hex digit represents 4 binary bits, making conversion between hex and binary especially direct. To convert hex to decimal, multiply each digit by 16 raised to its position power and sum the results.
Enter a number in hexadecimal, decimal, or binary format, and the calculator converts it to the other number systems, or performs arithmetic operations directly on hex values.
Example 1: Hexadecimal FF converts to decimal 255 (15×16 + 15 = 255).
Example 2: Hexadecimal 1A converts to binary 00011010.
Why is hexadecimal used in computing instead of just decimal? Hexadecimal maps neatly onto binary (4 bits per hex digit), making it much more compact and easier for programmers to read than long strings of 1s and 0s, while decimal doesn't align as cleanly with binary's base-2 structure.
What are common uses of hexadecimal in everyday computing? Hex is used to represent colors in web design (like #FF5733), memory addresses, error codes, and MAC addresses, among other technical identifiers.
Why do hex digits go up to F instead of stopping at 9? Since hexadecimal is base 16, it needs 16 distinct symbols; after using 0-9 for the first ten values, letters A through F represent the remaining six values (10 through 15).
How is hex related to binary? Each hexadecimal digit corresponds exactly to a group of 4 binary bits, making conversion between hex and binary simpler and less error-prone than converting between binary and decimal directly.
Can hexadecimal represent negative numbers? Yes, negative numbers in hex are typically represented using two's complement notation in computing systems, similar to how negative binary numbers are handled.