Base Calculator

Base Calculator - Add, Subtract, Multiply, or Divide Numbers of Any Base

This base calculator is designed to perform arithmetic operations on numbers represented in different base systems. With the help of our tool, you can also convert one base into another.

What is Base?

A base or radix indicates a count of different digits representing numbers within a positional numeral system.  

Types of Base:

There are four most common bases that include:

• Binary (base 2)
• Octal (base 8)
• Decimal (base 10)
• Hexadecimal (base 16)

Arithmetic Operations in Different Bases

Arithmetic operations (addition, subtraction, multiplication, and division) can be performed on different bases, but they need to understand the given below rules: 

Addition:

• Add the digits from right to left and convert them into decimal
• If the addition of values is less than the base then write the results 
• If the sum is greater or equal to the base, then write the remainder and carry quotient to the next column

Subtraction:

• Subtract the numbers from right to left 
• If the minuend is greater than or equals the subtrahend then write their difference 
• When the number is too small to subtract, borrow from the next large value and equal the base to the original digit. 

Multiplication:

• Similar to the decimal multiplications, but performed through the base calculations
• Use the partial values and sum up these digits together

Division:

• The base division is also similar to decimal division, but the calculations can be done under the base

In addition to the mathematical operations, the modulus operations are also considered by the base calculator. This modulus principle short form “mod” yields the remainder when a number is divided by the base. 

Mod:

The mod is used in the base number system to determine the remainder after division. It works with the data represented in various numeral systems. 

Binary, Decimal, Octal, Hexadecimal Equivalents