Decimal Calculator – Number Base Converter
Convert between decimal, binary, octal, and hexadecimal
Table of Contents
How to Use
- Enter a number in any base system
- Select the input base (decimal, binary, octal, or hex)
- Click calculate to see conversions to all bases
- View results in decimal, binary, octal, and hexadecimal
Understanding Number Systems
A number system is a way of representing numbers using a specific set of digits. Different number systems use different bases, which determine how many unique digits are available.
Common Number Systems
- Decimal (Base 10): Uses digits 0-9. This is the standard system we use in everyday life.
- Binary (Base 2): Uses only 0 and 1. Fundamental to computer systems and digital electronics.
- Octal (Base 8): Uses digits 0-7. Often used in computing as a more compact representation than binary.
- Hexadecimal (Base 16): Uses digits 0-9 and letters A-F. Widely used in programming and computer science.
Conversion Examples
Example: Converting Decimal 42
- Decimal: 42
- Binary: 101010
- Octal: 52
- Hexadecimal: 2A
Example: Converting Binary 11111111
- Binary: 11111111
- Decimal: 255
- Octal: 377
- Hexadecimal: FF
Real-World Applications
- Programming: Understanding memory addresses, bitwise operations, and data representation
- Computer Science: Algorithm design, data structures, and computational theory
- Digital Electronics: Circuit design and logic gates
- Networking: IP addresses and MAC addresses often use hexadecimal
- Color Codes: Web colors are represented in hexadecimal (e.g., #FF0000 for red)
- File Systems: Permissions and file attributes in Unix/Linux systems
- Debugging: Memory dumps and low-level debugging tools
Conversion Tips
Binary to Decimal
Multiply each digit by 2 raised to its position (from right, starting at 0), then sum the results.
Example: 1011₂ = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 8 + 0 + 2 + 1 = 11₁₀
Decimal to Binary
Repeatedly divide by 2 and record the remainders. Read the remainders from bottom to top.
Hexadecimal Shortcuts
Each hexadecimal digit represents exactly 4 binary digits (bits). This makes conversion between binary and hex very efficient.
Frequently Asked Questions
- Why do computers use binary?
- Computers use binary because digital circuits have two stable states: on (1) and off (0). This makes binary the most natural and reliable way to represent data in electronic systems. All computer operations ultimately reduce to binary calculations.
- What is hexadecimal used for?
- Hexadecimal is widely used in programming because it's more compact than binary while still being easy to convert. It's commonly used for memory addresses, color codes in web design, MAC addresses, and representing binary data in a human-readable format.
- How do I convert between binary and hexadecimal?
- Group binary digits into sets of 4 (from right to left), then convert each group to its hexadecimal equivalent. For example, 11010110₂ = 1101 0110 = D6₁₆. This works because 16 = 2⁴, so each hex digit represents exactly 4 binary digits.
- What's the difference between octal and decimal?
- Decimal uses base 10 (digits 0-9), while octal uses base 8 (digits 0-7). Octal was historically popular in computing because it's more compact than binary and each octal digit represents exactly 3 binary digits. However, hexadecimal has largely replaced it in modern computing.