How does base arithmetic work?

The calculator converts both input numbers from the given base to decimal (base 10), performs the arithmetic operation in decimal, and then converts the result back to the original base. This ensures accuracy for all supported bases.

What digits are valid for each base?

For base N, valid digits are 0 through N-1. For bases above 10, letters A through Z represent values 10 through 35. For example, hexadecimal (base 16) uses digits 0-9 and A-F. The calculator shows valid digits for the selected base.

Base Arithmetic Calculator - Add, Subtract, Multiply in

Q: What is base arithmetic?

Base arithmetic (or radix arithmetic) performs mathematical operations using a number system with a specific base. In base 2 (binary), digits are 0-1. In base 16 (hexadecimal), digits are 0-9 and A-F. This calculator converts numbers to decimal internally, performs the operation, and converts the result back to the original base.

Q: What bases are supported?

Any base from 2 (binary) to 36 is supported. Common bases include base 2 (binary), base 8 (octal), base 10 (decimal), and base 16 (hexadecimal). Bases above 10 use letters A-Z as additional digits.

Q: Can I use negative numbers?

Yes. Prefix a number with a minus sign (-) to indicate a negative number. The calculator handles negative numbers correctly for all operations.

Base Arithmetic Calculator

Perform addition, subtraction, and multiplication in any number base from 2 (binary) to 36. Results are shown in the selected base and decimal.

Arithmetic in Any Base

Base

Operation

Number 1

Number 2

Result

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How to Use the Base Arithmetic Calculator

Select the number base (2 to 36), choose an operation, and enter two numbers using the valid digits for that base. The calculator performs the operation and displays the result in both the selected base and decimal (base 10). For bases above 10, use letters A through Z for digits 10 through 35.

For example, in hexadecimal (base 16), FF + 1A = 119 (which is 255 + 26 = 281 in decimal).

Understanding Number Bases

A number base (or radix) determines how many unique digits are used to represent numbers. In our everyday decimal system (base 10), we use digits 0–9. In binary (base 2), only 0 and 1 are used. In hexadecimal (base 16), digits 0–9 and letters A–F are used.

Common Number Bases

Binary (base 2) is the language of computers, where each digit (bit) represents an on/off state. Octal (base 8) groups binary digits in threes, making it useful for Unix file permissions. Hexadecimal (base 16) groups binary digits in fours and is widely used for memory addresses, colour codes in CSS, and low-level programming.

How Base Conversion Works

To convert from base N to decimal, multiply each digit by N raised to its positional power and sum the results. For example, FF in hex = 15×16¹ + 15×16&sup0; = 240 + 15 = 255. Converting from decimal to base N requires repeated division by N and collecting remainders.

Frequently Asked Questions

What is base arithmetic?

Mathematical operations performed in a number system with a specific radix (base), such as binary, octal, or hexadecimal.

What bases are supported?

Any base from 2 (binary) to 36. Bases above 10 use letters A-Z as additional digits.

What digits are valid?

For base N, digits 0 through N-1. Hex uses 0-9 and A-F. The calculator displays valid digits for the selected base.

Can I use negative numbers?

Yes, prefix with a minus sign (-).

How accurate is the result?

Fully accurate for integer arithmetic. The calculator converts to decimal internally, performs the operation, and converts back.

Disclaimer: This calculator is for informational and educational purposes only. Results are estimates and should not be considered professional expert advice. Consult a qualified professional before making decisions based on these calculations. See our full Disclaimer.