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Base Calculator

Enter the values into the base calculator and click on “Calculate” to perform arithmetic operations across different base number systems (such as binary, octal, decimal, or hexadecimal). The tool will show the results in each selected base.

Operation:

Base:

First Number:

Operation:

Second Number:

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Base Calculator

This base calculator allows you to perform arithmetic operations on numbers in different base systems. It also helps you convert numbers from one base to another, making calculations in binary, octal, decimal, and hexadecimal easier.

What is a Base?

A base (or radix) represents the number of unique digits used in a positional numeral system. For example:

Decimal (Base 10) uses digits 0–9
Binary (Base 2) uses digits 0–1
Octal (Base 8) uses digits 0–7
Hexadecimal (Base 16) uses digits 0–9 and A–F

Common Bases:

Binary (Base 2)
Octal (Base 8)
Decimal (Base 10)
Hexadecimal (Base 16)

Arithmetic Operations in Different Bases

Addition

Add digits from right to left.
If the sum is less than the base, write it directly.
If the sum is equal to or greater than the base, write the remainder and carry the quotient to the next column.

Subtraction

Subtract digits from right to left.
If the minuend is greater than or equal to the subtrahend, write the difference.
If the minuend is smaller, borrow from the next higher digit, adding the base to the current digit.

Multiplication

Perform as in decimal multiplication, but all calculations are done in the given base.
Multiply digits, sum partial results, and convert according to the base.

Division

Division works similarly to decimal division but calculations are done within the base system.

Modulus (Mod)

The mod operation gives the remainder after dividing a number by the base. It is widely used in computing and base conversions.

Binary, Decimal, Octal, and Hexadecimal Equivalents

Binary (Base 2)	Decimal (Base 10)	Octal (Base 8)	Hexadecimal (Base 16)
0	0	0	0
1	1	1	1
10	2	2	2
11	3	3	3
100	4	4	4
101	5	5	5
110	6	6	6
111	7	7	7
1000	8	10	8
1001	9	11	9
1010	10	12	A
1011	11	13	B
1100	12	14	C
1101	13	15	D
1110	14	16	E
1111	15	17	F
10000	16	20	10
10001	17	21	11
10010	18	22	12
10011	19	23	13
10100	20	24	14

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