About

In software engineering and digital electronics, data isn't always represented in decimal (Base-10). Memory addresses are typically Hexadecimal (Base-16), file permissions are often Octal (Base-8), and low-level logic is Binary (Base-2). This "Swiss Army Knife" calculator allows developers and students to sum numbers from different bases without manual conversion. It normalizes all inputs to a common arbitrary-precision integer before converting the result back to your target base.

The mathematical principle relies on positional notation where a digit d at position i contributes d × bⁱ to the value. For systems involving bases greater than 10, letters A-Z represent values from 10 to 35. This tool handles these alphanumerics automatically and prevents syntax errors by disabling invalid keys for the selected base.

Formulas

The value of a number in any base b is calculated as:

V = n∑i=0 (d_i × bⁱ)

For example, adding Hex A1 and Binary 10:

A1₁₆ + 10₂ = (10×16¹ + 1×16⁰) + (1×2¹ + 0×2⁰) = 161 + 2 = 163₁₀

Reference Data

Decimal (10)	Binary (2)	Octal (8)	Hexadecimal (16)	Base-36
0	0	0	0	0
5	101	5	5	5
10	1010	12	A	A
15	1111	17	F	F
16	10000	20	10	G
35	100011	43	23	Z
100	1100100	144	64	2S
255	11111111	377	FF	73

Frequently Asked Questions

This tool supports up to Base-36. This is because we use standard digits 0-9 (10 symbols) and the English alphabet A-Z (26 symbols), totaling 36 unique symbols.

Yes. This tool is designed for mixed-base arithmetic. You can set the first input to Hexadecimal and the second to Binary; the calculator normalizes them to perform the addition.

The Octal system is Base-8, meaning it only uses digits 0 through 7. The digit "8" or "9" does not exist in Octal, just as there is no single digit for "10" in Decimal. The tool blocks invalid inputs to prevent syntax errors.

The calculator uses BigInt logic internally, allowing for computations that exceed the standard 32-bit or 64-bit integer limits found in many standard calculators.