1 & 1 = 1, all others = 0
0 | 0 = 0, all others = 1
Same bits = 0, different = 1
Flips all bits: 0→1, 1→0
Hex Mode: Enter hexadecimal values with or without the 0x prefix. Valid characters: 0-9, A-F.
Decimal Mode: Enter standard decimal integers. Negative numbers use two's complement representation.
Examples: 0xFF, FF, 1A3, 0x1234ABCD
Hexadecimal (base-16) is a positional numeral system that uses sixteen distinct symbols: 0-9 for values zero to nine, and A-F for values ten to fifteen. It is widely used in computing and digital electronics because it provides a human-friendly representation of binary-coded values. Each hexadecimal digit represents exactly four binary bits (a nibble), making conversion between hex and binary straightforward.
Hexadecimal is commonly used for memory addresses, color codes in web design (e.g., #FF5733), MAC addresses, and representing byte values in assembly language and low-level programming. Understanding hex arithmetic and bitwise operations is essential for systems programming, embedded development, and computer security.
This calculator supports both arithmetic operations (addition, subtraction, multiplication, division, modulo, exponentiation) and bitwise operations (AND, OR, XOR, NOT, left shift, right shift). You can input values in either hexadecimal or decimal format using the toggle switch.
The bit width setting determines the maximum value and how overflow/underflow is handled. For example, 8-bit mode limits values to 0-255, while 32-bit mode allows values up to 4,294,967,295. Negative results are represented using two's complement notation within the selected bit width.
Disclaimer
Hexadecimal calculations are based on standard arithmetic and bitwise rules. Results may be limited by selected bit-width and signed/unsigned settings. This calculator is intended for educational and reference purposes.