Hex Calculator
Perform arithmetic operations directly in Hexadecimal (Base-16). Instantly convert results to binary, octal, and decimal with positional weightings.
Hexadecimal Result (Base-16)
0xCE
Multi-Base Representation Matrix
Conversion & Arithmetic Log
Understanding Hexadecimal (Base-16) Math
The hexadecimal positional numeral system utilizes a radix (base) of 16. It uses 16 distinct symbols: the standard digits 0-9 to represent values from zero to nine, and the letters A-F (or a-f) to represent values from ten to fifteen.
Hexadecimal is widely used in computer science and digital electronics because it provides a human-friendly representation of binary-coded values. A single hex digit represents a nibble (4 bits), and a pair of hex digits represents an 8-bit byte (from 0x00 to 0xFF).
How Hexadecimal Math Works
To perform arithmetic directly in hex, you can either construct carrying/borrowing tables in Base-16, or convert the values into decimal (Base-10), perform standard arithmetic, and then convert the result back to Base-16:
- Hex to Decimal: Expand the number by multiplying each digit by its positional power of 16. For example:
1A= 1 × 161 + 10 × 160 = 16 + 10 = 26. - Decimal to Hex: Divide the decimal number repeatedly by 16 and track the remainder. For example, to convert 206 back to hex: 206 / 16 = 12 remainder 14 (which represents
E), and 12 / 16 = 0 remainder 12 (which representsC). Reading the remainders from bottom to top givesCE.
Frequently Asked Questions About Hexadecimal
What are the values of A, B, C, D, E, F in hexadecimal?
In the hexadecimal system (Base-16), the letters A through F represent decimal values from 10 to 15, respectively: A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.
How does the calculator perform hex subtraction?
The calculator converts both hexadecimal inputs into their decimal values, performs the subtraction in decimal, and then converts the resulting value back into a hexadecimal string.
How do you convert a hex number to binary?
To convert a hexadecimal number to binary, you can translate each hex digit directly into its equivalent 4-bit binary sequence. For example, the hex digit 'A' corresponds to binary '1010', and 'F' corresponds to '1111'.
Can this convert hex to other bases?
Yes. Instantly convert hexadecimal to binary, octal, and decimal with step-by-step logs.