About

Standard calculators operate strictly in Base-10 (Decimal). However, computer science utilizes Binary (Base-2), Octal (Base-8), and Hexadecimal (Base-16) for memory addressing, bitwise logic, and color encoding. Performing arithmetic between these systems manually is error-prone due to carry-over complexity and notation differences.

This tool acts as a multi-base engine. It treats inputs as native values in their respective bases, performs the operation using high-precision logic, and renders the result across all four systems simultaneously. It supports fractional values (e.g., 10.11₂) which are critical for understanding floating-point representation standards like IEEE 754.

Formulas

The calculator converts all inputs to a standardized internal high-precision decimal format before processing.

General Base Expansion:

N_b = n∑i=-m d_i × bⁱ

For binary fraction 10.11₂:

(1×2¹) + (0×2⁰) + (1×2^-1) + (1×2^-2) = 2.75₁₀

Reference Data

Decimal (10)	Binary (2)	Octal (8)	Hexadecimal (16)
0	0000	0	0
1	0001	1	1
2	0010	2	2
3	0011	3	3
4	0100	4	4
5	0101	5	5
6	0110	6	6
7	0111	7	7
8	1000	10	8
9	1001	11	9
10	1010	12	A
11	1011	13	B
12	1100	14	C
13	1101	15	D
14	1110	16	E
15	1111	17	F

Frequently Asked Questions

Fractional parts are calculated by successive multiplication (for Decimal to Base-N) or division (Base-N to Decimal). Note that exact representations in one base (like 0.1 in Decimal) may result in repeating fractions in another (Binary), leading to precision truncation.

The engine uses BigInt logic for integers, supporting practically unlimited digits. Floating-point operations are limited to 10 decimal places of precision to ensure UI responsiveness.

This is due to the IEEE 754 standard. 0.1 and 0.2 cannot be exactly represented in binary, similar to 1/3 in decimal. The tiny rounding errors accumulate.

Yes. The tool allows you to input the first number in Hexadecimal and the second in Binary. The logic normalizes them before the operation.