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Decimal Number System Converter

Convert decimal (Base-10) numbers to binary, octal, hexadecimal, and bases up to 36. An educational tool for understanding positional notation.

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About

Positional notation is the backbone of modern mathematics and computing. While humans naturally count in Base-10 (Decimal) due to having ten fingers computers operate in Base-2 (Binary) or Base-16 (Hexadecimal). This converter breaks down the translation process between these systems. It helps students and developers understand how integer values are represented across different radixes.

The tool utilizes the division algorithm for integers where the number is repeatedly divided by the target base. The remainders of these divisions correspond to the digits in the new base starting from the least significant digit. This visualization is essential for debugging low-level code or solving problems in discrete mathematics.

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Formulas

To convert a decimal number d to a base b we use Euclidean division repeatedly. We find integer q and remainder r such that:

d = q × b + r

Where 0 ≤ r < b. The process repeats using q as the new dividend until q becomes 0. The sequence of remainders read in reverse order forms the new number.

Reference Data

Decimal N10Binary N2Hex N16Description
100011Unit
101010ABase of Decimal
151111FMax 4-bit Value
161000010Base of Hex
25511111111FFMax Byte Value

Frequently Asked Questions

Binary numbers become incredibly long and difficult for humans to read. Hexadecimal is a compact shorthand for binary. One hex digit exactly represents four binary digits (bits) making memory addresses and color codes easier to manage.
Base-36. This system uses digits 0-9 followed by letters A-Z. Base-36 is often used in URL shortening algorithms to compress large database IDs into short alphanumeric strings.
In positional systems with a base greater than 10 standard Arabic numerals (0-9) are insufficient. Letters are used as substitutes: A=10, B=11, C=12, up to Z=35.