What is a base converter?

A base converter is a tool that converts the representation of a number from one numeral system to another, such as from binary to decimal, decimal to hexadecimal, or between any bases from 2 to 36.

Which number bases does this base converter support?

This base converter supports all integer bases from 2 to 36, including binary (base 2), octal (base 8), decimal (base 10), hexadecimal (base 16) and many other custom bases.

Does this base converter handle fractional numbers?

Yes. You can enter a decimal point in your number, for example 101.11 in base 2 or 3A.F in base 16. The tool converts both the integer part and the fractional part, showing the result in the target base with a limited number of fractional digits.

How accurate is the conversion for large or fractional numbers?

For integers the converter uses exact arithmetic, so the conversion is precise as long as the number fits in the browser's memory limits. For fractional parts, it uses floating-point arithmetic with a capped number of digits after the point, which is more than sufficient for most educational and engineering uses.

Where are base conversions used in practice?

Base conversions appear in computer science, digital electronics, cryptography and data encoding. Programmers convert between binary, hexadecimal and decimal all the time when working with memory addresses, bit masks, color codes, network protocols and low-level debugging.

Base Converter – Convert Between Binary, Octal, Decimal & Hex

What is a number base?

A number base (or radix) is the number of distinct digits used to write numbers in a positional numeral system. In everyday life we mostly use base 10 (decimal), which has digits 0–9. Computers, however, naturally work in base 2 (binary).

In any base \(b\), digits run from 0 up to \(b - 1\). For bases above 10, we use letters A, B, C, … to represent values 10, 11, 12, and so on. For example, in base 16:

A = 10, B = 11, C = 12, D = 13, E = 14, F = 15

Place-value representation

Any number in base \(b\) can be written as a sum of powers of \(b\). For example, the decimal number 57 in base 10 can be written as:

57 = 5 × 10² + 7 × 10⁰

In base 2, the binary number 1011₂ represents:

1011₂ = 1 × 2³ + 0 × 2² + 1 × 2¹ + 1
                  × 2⁰ = 11₁₀

Integer part and fractional part

When a decimal point is present, the part to the left is the integer part, and the part to the right is the fractional part. In base \(b\), a number like

dₖ … d₂ d₁ d₀ . f₁ f₂ … fₙ

corresponds to

\(dₖ b^k + \dots + d₂ b² + d₁ b¹ + d₀ b⁰ + f₁ b^{-1} + f₂ b^{-2} + \dots + fₙ b^{-n}\)

How base conversion works

Converting between bases typically happens in two conceptual steps:

Convert the original representation to an internal decimal value.
Convert that decimal value to the target base.

Step 1 – from base \(b\) to decimal

To convert from an arbitrary base \(b\) to decimal, you multiply each digit by its positional weight (a power of \(b\)) and sum everything. For example, converting 7F₁₆ to decimal:

7F₁₆ = 7 × 16¹ + 15 × 16⁰ = 7 × 16 + 15 =
                  127₁₀

Step 2 – from decimal to base \(b\)

To convert a decimal integer N to base \(b\), repeatedly divide by \(b\) and collect remainders:

Divide N by \(b\). The remainder is the least significant digit.
Replace N with the quotient and repeat until the quotient is 0.
Read the remainders from last to first; this gives the digits in the new base.

For the fractional part, you do the opposite: repeatedly multiply by \(b\) and collect the integer part at each step.

Common number bases

Binary (base 2): digits 0–1. Used internally by all digital hardware.
Octal (base 8): digits 0–7. Historically used in some systems; still appears in permissions in Unix.
Decimal (base 10): digits 0–9. The standard numeral system for everyday arithmetic.
Hexadecimal (base 16): digits 0–9 and A–F. Very common in programming, memory addresses, color codes and networking.

Using this base converter effectively

Enter the number exactly as it is written in its original base.
Select the correct From base and To base.
Click Convert number and review the main output and the quick “Binary–Octal–Decimal–Hex” panel.
Compare the converter’s result with manual calculations to build confidence and intuition.

Base converter – FAQ

A base converter is a digital tool that rewrites the same numeric value using a different numeral system. For example, it can show that 255₁₀ is the same value as FF₁₆, 11111111₂ and 377₈.

The selector allows any integer base from 2 up to 36. That includes binary (2), octal (8), decimal (10), hexadecimal (16) and many other custom bases that appear in coding puzzles or specialised algorithms.

Yes. You can start the number with a minus sign for negative values, and you may include one decimal point to represent fractions (for example -101.11 in base 2 or 3A.F in base 16). The converter processes both the integer and fractional parts.

The calculator validates your input and shows a clear error message if a digit is not allowed in the selected base (for example, using 8 in base 8 or G in base 16). Correct the digit or change the base and try again.

Base conversions are everywhere in computing: encoding and decoding data, working with bitmasks, reading memory dumps, interpreting color codes, writing low-level drivers and debugging network protocols. Being fluent with binary, decimal and hexadecimal is a core skill for developers and computer engineers.

Base Converter

Interactive base converter

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