Hexadecimal Calculator
Perform operations on hexadecimal numbers
Hexadecimal Calculator: Simplify Hex Operations
Hexadecimal, or base-16, is a numbering system widely used in computer science and digital electronics. It provides a more compact representation of binary numbers, making it easier for humans to read and write large binary values. Our **Hexadecimal Calculator** allows you to perform basic arithmetic operations (addition, subtraction, multiplication, and division) directly on hexadecimal numbers, streamlining your workflow and reducing errors.
Quick Fact: Hexadecimal uses 16 unique symbols: 0-9 for values zero to nine, and A-F for values ten to fifteen. Each hexadecimal digit represents exactly four binary digits (bits).
What are Hexadecimal Numbers?
The hexadecimal system is a positional numeral system with a base (radix) of 16. It uses 16 distinct symbols, which are the digits 0 through 9, and the letters A, B, C, D, E, F (or a, b, c, d, e, f). Each hexadecimal digit corresponds to a 4-bit binary sequence.
- Decimal 0-9 are Hex 0-9
- Decimal 10 is Hex A
- Decimal 11 is Hex B
- Decimal 12 is Hex C
- Decimal 13 is Hex D
- Decimal 14 is Hex E
- Decimal 15 is Hex F
- Decimal 16 is Hex 10 ($1 \times 16^1 + 0 \times 16^0$)
How to Use Our Hexadecimal Calculator
Our user-friendly **Hexadecimal Calculator** makes hexadecimal arithmetic straightforward. Follow these simple steps:
- Enter Hex Number 1: Input your first hexadecimal number into the “Hex Number 1” field. Ensure it contains only valid hex digits (0-9, A-F, case-insensitive).
- Enter Hex Number 2: Input your second hexadecimal number into the “Hex Number 2” field.
- Select an Operation: Choose the arithmetic operation you wish to perform: Addition (+), Subtraction (-), Multiplication (×), or Division (÷).
- Click “Calculate”: The calculator will process the hexadecimal inputs based on your chosen operation and display the hexadecimal result.
- Click “Clear Inputs” (Optional): To start a new calculation, use this button to clear the input fields and result.
Hexadecimal Arithmetic Basics
While our calculator handles the computation, understanding the underlying principles of hexadecimal arithmetic is beneficial:
Hexadecimal to Decimal Conversion
To convert a hexadecimal number to decimal, multiply each digit by 16 raised to the power of its position (starting from 0 on the right).
Example: $A5_{16} = (10 \times 16^1) + (5 \times 16^0) = 160 + 5 = 165_{10}$
Decimal to Hexadecimal Conversion
To convert a decimal number to hexadecimal, repeatedly divide the decimal number by 16 and record the remainders. Read the remainders from bottom to top.
Example: $165_{10}$
- $165 \div 16 = 10$ remainder $5$
- $10 \div 16 = 0$ remainder $10$ (which is ‘A’ in hex)
Reading from bottom to top: $A5_{16}$
Performing Operations
Hexadecimal addition, subtraction, multiplication, and division can be performed by converting the hex numbers to their decimal equivalents, performing the operation, and then converting the decimal result back to hexadecimal. Our calculator automates this entire process for you.
| Operation | Description | Example |
|---|---|---|
| Addition | Sum of two hex numbers. | $A_{16} + 5_{16} = F_{16}$ (10 + 5 = 15) |
| Subtraction | Difference between two hex numbers. | $F_{16} – 5_{16} = A_{16}$ (15 – 5 = 10) |
| Multiplication | Product of two hex numbers. | $A_{16} \times 2_{16} = 14_{16}$ (10 × 2 = 20, $20_{10} = 1 \times 16^1 + 4 \times 16^0 = 14_{16}$) |
| Division | Quotient of two hex numbers (integer division). | $F_{16} \div 3_{16} = 5_{16}$ (15 ÷ 3 = 5) |
Applications of Hexadecimal Calculations
Hexadecimal numbers are indispensable in various fields, especially those related to computing:
- Memory Addresses: Used to represent memory locations in computers.
- Color Codes: HTML color codes (e.g., #FF00FF for magenta) are expressed in hexadecimal.
- MAC Addresses: Unique identifiers for network interfaces are typically written in hexadecimal.
- Debugging: Programmers often use hex dumps to inspect the raw contents of memory or files.
- Assembly Language: Used to specify immediate values and addresses in assembly code.
Important Note: Our calculator performs integer division for the division operation, meaning any remainder will be discarded, similar to how integer division works in many programming languages.
Our **Hexadecimal Calculator** is an essential tool for developers, network engineers, students, and anyone working with low-level data. It ensures accuracy and saves time, whether you’re debugging code, configuring networks, or simply learning about number systems.