About

In digital forensics, low-level programming, and network engineering, arithmetic often bridges multiple number systems. A developer might need to multiply a Hexadecimal memory offset by an Octal block size. Doing this manually involves error-prone intermediate conversion to Decimal.

This utility automates cross-base multiplication. It accepts two inputs with independent bases (from Binary Base-2 to Base-36) and projects the result into a third user-defined base. It handles standard ASCII alphanumerics (0-9, A-Z) where "A" represents 10 and "Z" represents 35, validating inputs to ensure no illegal characters exist for the selected radix.

Formulas

The calculator performs a three-step transformation:

1. Normalize to Integer:

N = k∑i=0 d_i × baseⁱ

2. Arithmetic Operation:

Result₁₀ = N₁ × N₂

3. Encode to Target Base:

Repeatedly compute R = Result % TargetBase

Reference Data

Base	Name	Valid Digits	Typical Use
2	Binary	0-1	Machine Code, logic gates
8	Octal	0-7	Unix file permissions (chmod)
10	Decimal	0-9	Standard Human Arithmetic
16	Hexadecimal	0-9, A-F	Colors, Memory Addresses, IPv6
32	Base32	A-Z, 2-7	Encoding binary data
36	Base36	0-9, A-Z	URL Shortening, Compact IDs

Frequently Asked Questions

Yes. Set Input 1 to Base 16 (Hex) and Input 2 to Base 2 (Binary). The tool converts both to a common BigInt format, multiplies them, and formats the output to your chosen result base.

Hexadecimal only supports 0-9 and A-F. The letter "G" is the 16th digit (value 16) and is only valid in Base-17 or higher. The calculator will strip invalid characters or return an error.

Currently, this tool focuses on unsigned integer arithmetic standard in computing contexts (addressing, bitmasks). Negative inputs are treated as absolute values or parsed strictly as alphanumeric strings.