About

In systems programming and memory management, converting between numerical bases is a daily necessity. This tool provides immediate conversion between the four primary numbering systems used in computing: Decimal (Base 10), Binary (Base 2), Hexadecimal (Base 16), and Octal (Base 8). Unlike standard calculators that fail with integers exceeding 64 bits, this engine utilizes arbitrary-precision logic to handle inputs of any length, essential for cryptographic hashes or memory address mapping.

Beyond simple conversion, the tool supports bitwise arithmetic. Developers can perform logical AND, OR, XOR, and NOT operations directly in their preferred base. This functionality is critical when debugging bitmasks, setting permission flags, or analyzing raw data packets where binary alignment dictates functionality.

Formulas

Conversions rely on positional notation where a number N in base b is the sum of its digits d multiplied by their respective powers of the base.

N = n∑i=0 d_i × bⁱ

For example, Hexadecimal AF to Decimal:

AF₁₆ = 10 × 16¹ + 15 × 16⁰ = 175₁₀

Reference Data

Decimal (10)	Binary (2)	Hexadecimal (16)	Octal (8)
0	0000	0	0
1	0001	1	1
5	0101	5	5
10	1010	A	12
15	1111	F	17
16	10000	10	20
255	11111111	FF	377
1024	10000000000	400	2000

Frequently Asked Questions

Yes. This tool uses BigInt logic, allowing for calculations on numbers far exceeding the standard 64-bit integer limit (9 quintillion). You can input 256-bit or even 4096-bit keys without precision loss.

Bitwise operations (AND, OR, XOR) treat the inputs as sequences of bits (0s and 1s) rather than numerical values. For example, XOR sets a bit to 1 only if the input bits are different.

Hexadecimal is a compact representation of binary. One hex digit represents exactly four binary bits (a nibble). This makes reading memory addresses or color codes significantly easier for humans than parsing long strings of zeros and ones.

This calculator operates primarily on unsigned integers for bitwise logic. Negative numbers in computing are typically represented using Two's Complement, which depends on a fixed bit-width (e.g., 32-bit vs 64-bit), making a generic "negative" conversion ambiguous without defining the word size.