Number Base Arithmetic Calculator

This number base arithmetic calculator adds, subtracts or multiplies two numbers written in a base other than ten, such as binary, octal, duodecimal or hexadecimal. Enter the two numbers, choose the operation and the base, and the calculator returns the answer in that same base, with the decimal value shown for checking. Working directly in another base is handy in computing and digital electronics, where binary and hexadecimal are everywhere, and it builds a feel for how place value works in any base. The calculator flags any digit that is not valid for the chosen base. The method, a worked example and the assumptions are below.

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First number

Second number

Operation

Base

Result (decimal)

Base

The formula

Each number is read in the chosen base, the operation is carried out, and the result is written back in that base. A digit must be less than the base, so base 2 allows only 0 and 1, base 16 allows 0 to 9 and A to F.

Worked example

In binary, 1010 + 11 means 10 + 3 in decimal, which is 13, written 1101 in binary. Enter 1010 and 11 with base 2 and plus to confirm.

Frequently asked questions

What bases can I use?

This tool offers base 2, 8, 12 and 16, the most common non-decimal bases in computing and maths.

What if I type an invalid digit?

The calculator flags it. Each digit must be smaller than the base, so 2 is not allowed in binary.

Why show the decimal too?

So you can check the result, since most people read decimal more easily than other bases.

Who this calculator is for

This calculator is for students, programmers and anyone needing a quick, reliable result.

What this calculator assumes

You enter valid input.
The standard algorithm is applied.
Results are rounded for display.

Formula and sources

Related calculators

Scientific Calculator: general scientific maths.
Percentage Calculator: percentages and changes.
Prime Factorisation Calculator: factor a number into primes.

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