Base N converter
Convert base nconverter between units instantly. Includes conversion tables, common equivalents, and calculation formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Base N converter
Calculator
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Formula: Decimal = sum of (digit x base^position); Target = repeated division by target base
Worked example โ 255 (base 10) = FF (base 16)
Formula
Decimal = sum of (digit x base^position); Target = repeated division by target base
Convert to decimal by multiplying each digit by the source base raised to the power of its position (rightmost is 0) and summing. Then convert from decimal to the target base by repeatedly dividing by the target base and collecting remainders in reverse order.
Worked Examples
Example 1: Decimal to Hexadecimal
Problem:Convert decimal 255 to hexadecimal (base 16).
Solution:255 / 16 = 15 remainder 15 (F) 15 / 16 = 0 remainder 15 (F) Reading remainders bottom to top: FF
Result:255 (base 10) = FF (base 16)
Example 2: Binary to Octal
Problem:Convert binary 11010110 to octal (base 8).
Solution:First convert binary to decimal: 1x128 + 1x64 + 0x32 + 1x16 + 0x8 + 1x4 + 1x2 + 0x1 = 214 Then 214 to octal: 214 / 8 = 26 r 6, 26 / 8 = 3 r 2, 3 / 8 = 0 r 3 Result: 326
Result:11010110 (base 2) = 326 (base 8)
Frequently Asked Questions
What is a number base or radix?
A number base (also called radix) is the number of unique digits used to represent numbers in a positional numeral system. Base 10 (decimal) uses digits 0-9, base 2 (binary) uses 0-1, base 16 (hexadecimal) uses 0-9 and A-F. Each position in a number represents a power of the base. For example, 42 in base 10 means 4 times 10 to the first power plus 2 times 10 to the zero power, equaling forty-two.
How do I convert between any two bases?
The standard approach is a two-step process. First, convert the source number to base 10 (decimal) by multiplying each digit by its positional power of the source base and summing the results. Second, convert the decimal value to the target base by repeatedly dividing by the target base and collecting remainders. This converter handles both steps automatically for any base from 2 to 36.
Why is base 16 (hexadecimal) commonly used in computing?
Hexadecimal is popular in computing because it provides a compact representation of binary data. Each hex digit corresponds to exactly 4 binary bits, so one byte (8 bits) is represented by exactly two hex digits. This makes it easy to read and write memory addresses, color codes (like FF0000 for red), and byte values. Compared to binary, hex reduces the length of a representation by a factor of four while maintaining a simple digit-to-bits mapping.
What bases are supported by this converter?
This converter supports any base from 2 to 36. Bases 2 through 10 use numeric digits 0-9 as needed. Bases 11 through 36 extend the digit set with letters A through Z, where A represents 10, B represents 11, and so on up to Z representing 35. Common bases include binary (2), octal (8), decimal (10), duodecimal (12), hexadecimal (16), and base 36 which is the maximum single-character digit base.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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