Hexadecimal Calculator
Convert numbers between decimal, binary, octal, and hexadecimal systems
Table of Contents
How to Use
- Enter the number you want to convert
- Select the input number system (decimal, binary, octal, or hexadecimal)
- Select the output number system
- Click calculate to see the converted value
- View all number system representations
What are Number Systems?
Number systems are different ways of representing numbers using a specific set of digits. The most common systems are decimal (base 10), binary (base 2), octal (base 8), and hexadecimal (base 16).
Each system uses a different base, which determines how many unique digits are available. For example, decimal uses digits 0-9, while hexadecimal uses digits 0-9 and letters A-F.
Number Systems Explained
- Decimal (Base 10): Uses digits 0-9. This is the standard number system we use daily.
- Binary (Base 2): Uses digits 0 and 1. Essential for computer systems and digital electronics.
- Octal (Base 8): Uses digits 0-7. Sometimes used in computing and programming.
- Hexadecimal (Base 16): Uses digits 0-9 and letters A-F. Widely used in programming and computer science.
Conversion Methods
Converting between number systems typically involves two steps:
- Convert the input number to decimal (base 10)
- Convert the decimal number to the desired output base
This two-step process ensures accuracy and makes it easier to convert between any two number systems.
Frequently Asked Questions
- What is hexadecimal used for?
- Hexadecimal is commonly used in programming, computer science, and digital electronics. It's particularly useful for representing memory addresses, color codes, and binary data in a more readable format.
- How do I convert binary to hexadecimal?
- Group binary digits into sets of 4 (starting from the right), then convert each group to its hexadecimal equivalent. For example, 11010110 becomes D6 in hexadecimal.
- What are the valid digits for each number system?
- Decimal: 0-9, Binary: 0-1, Octal: 0-7, Hexadecimal: 0-9 and A-F (where A=10, B=11, C=12, D=13, E=14, F=15).
- Why is hexadecimal preferred in programming?
- Hexadecimal is preferred because it's more compact than binary (4 binary digits = 1 hexadecimal digit) and easier to read than long binary strings. It also aligns well with byte boundaries in computer systems.