AI Math Assistant
BetaAsk questions about your calculation results
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AI provides general assistance. Always verify important calculations.
About This Calculator
Hexadecimal is a base-16 number system using digits 0-9 and letters A-F, widely adopted in computing because it maps cleanly to binary in groups of four bits. It's used extensively in color codes, memory addresses, MAC addresses, and low-level programming. This calculator performs hex arithmetic and converts between hexadecimal, decimal, binary, and octal representations.
Quick Tips
- 1 Each hex digit represents exactly 4 binary bits, making conversion simple.
- 2 FF in hex equals 255 in decimal — the max value of one byte.
- 3 Prefix hex numbers with 0x in programming to distinguish from decimal values.
Example Calculation
Add hex values 0x1A3F and 0x0B21.
0x1A3F + 0x0B21 = 0x2560 | Decimal: 6719 + 2849 = 9568
Understanding Hexadecimal Numbers
Hexadecimal (base-16) uses digits 0-9 and letters A-F to represent values 0-15. It is widely used in computing because each hex digit represents exactly 4 binary digits (bits), making it a compact way to express binary data. For example, the decimal number 255 is FF in hex and 11111111 in binary. Hex is ubiquitous in color codes (#FF0000), memory addresses, and data encoding.
Converting Between Number Systems
This calculator takes decimal inputs and displays results in four number systems: decimal (base-10), hexadecimal (base-16), binary (base-2), and octal (base-8). Enter decimal numbers and the calculator converts them to hex and other bases automatically. For example, entering 255 shows FF in hex, 11111111 in binary, and 377 in octal.
Frequently Asked Questions
Hex is compact and maps cleanly to binary — each hex digit represents exactly 4 bits. A byte (8 bits) is always two hex digits (00-FF). This makes hex much easier to read than long binary strings while remaining close to the underlying binary representation. It is used for memory addresses, color codes, and debugging.
Multiply each hex digit by its place value (powers of 16, right to left) and add them up. For FF: F×16 + F×1 = 15×16 + 15×1 = 240 + 15 = 255. For A0: A×16 + 0×1 = 10×16 + 0 = 160.
Hexadecimal uses base 16 (digits 0-F) and each digit represents 4 bits. Octal uses base 8 (digits 0-7) and each digit represents 3 bits. Hex is more commonly used today because it aligns with byte boundaries (8 bits = 2 hex digits), while octal was historically used on systems with 12, 24, or 36-bit word sizes.