What Is Radix Conversion?
Radix conversion means expressing the same numerical value using a different number base, or radix. People commonly use the base-10 decimal system in everyday life, while digital systems use binary representation as a fundamental way of representing information and logic states. Converting between number bases is useful in programming, digital electronics, networking, computer science, and technical education.
This tool allows you to convert values between common number bases directly in your web browser. No software installation is required, and the calculations are performed locally in your browser.
Characteristics and Common Uses of Each Number Base
- Binary (Base 2): Uses only the digits 0 and 1. Binary representation is fundamental to digital logic, bitwise operations, flags, and computer hardware.
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Octal (Base 8):
Uses the digits 0 through 7.
One octal digit corresponds to three binary digits, and octal notation is commonly encountered in Unix and Linux file permissions such as
chmod 755. - Decimal (Base 10): Uses the digits 0 through 9. It is the standard number system used for everyday calculations, measurements, financial values, and general counting.
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Hexadecimal (Base 16):
Uses the digits 0 through 9 and the letters A through F.
One hexadecimal digit represents four binary digits, making hexadecimal useful for compactly representing binary data, memory addresses, and web color values such as
#FFFFFF.
How Radix Conversion Works
Converting from Base-n to Decimal
To convert a number from another base to decimal, multiply each digit by the corresponding power of the original base and then add the results together. The rightmost digit has a positional value of 0, the next digit has a positional value of 1, and so on.
Example: Binary 1011 to Decimal
(1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = 8 + 0 + 2 + 1 = 11Converting from Decimal to Base-n
To convert a decimal integer to another base, repeatedly divide the number by the target base and record the remainder from each division. Reading the remainders from the last division back to the first produces the converted value. This tool can be used to quickly check the result of manual calculations.
Why Are Multiple Number Bases Used?
Different number bases are useful for different types of work. Binary is closely related to digital logic and computer hardware, while hexadecimal provides a shorter and more readable representation of binary values. Octal is still encountered in Unix and Linux permissions, and decimal remains the most familiar system for everyday numerical values.
Frequently Asked Questions (FAQ)
A. In hexadecimal, the letters A through F represent the values 10 through 15. The sequence is A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15.
A. The tool uses JavaScript's standard Number type for calculations.
Integer values can be represented exactly up to Number.MAX_SAFE_INTEGER, which is 9,007,199,254,740,991.
Values beyond this range may not be represented exactly and can produce inaccuracies in lower digits.
A. No. The tool is free to use and does not require account registration or software installation.
A. No. The conversion calculations are performed directly in your browser, and the values entered into the tool are not uploaded to our servers as part of the calculation process. This allows you to perform conversions without sending your input data to a remote processing service.
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