About

In systems programming and memory management, precise data representation is non-negotiable. This Number System Converter facilitates the translation of values across different radices, specifically targeting the core bases used in computing: Binary (base-2), Octal (base-8), Decimal (base-10), and Hexadecimal (base-16). Unlike simple integer converters, this tool handles fractional parts (e.g., 10.101 in binary) and supports arbitrary precision logic for large datasets.

Misinterpreting a hex dump or an octal permission bitmask can lead to critical security vulnerabilities or segmentation faults. Engineers use this tool to verify memory addresses, decode instruction sets, and perform bitwise arithmetic verification without manual errors. The engine supports bases ranging from 2 to 36, utilizing the full alphanumeric spectrum for higher radices.

Formulas

The value of a number N in base b with digits d is calculated using positional notation:

n∑i=-m d_i ⋅ bⁱ

For example, converting Hexadecimal 2F.8 to Decimal:

(2 × 16¹) + (15 × 16⁰) + (8 × 16^-1) = 47.5

Reference Data

Decimal (10)	Binary (2)	Hexadecimal (16)	Octal (8)	Description
0	0000	0x0	0	Null / Zero
1	0001	0x1	1	Start bit
10	1010	0xA	12	Line Feed (LF)
15	1111	0xF	17	Max 4-bit Value
127	0111 1111	0x7F	177	Max Signed 8-bit
255	1111 1111	0xFF	377	Max Unsigned 8-bit
1024	100 0000 0000	0x400	2000	1 Kilobyte (Binary)
65535	1111 ... 1111	0xFFFF	177777	Max Unsigned 16-bit

Frequently Asked Questions

In a base-8 (Octal) system, the only valid digits are 0 through 7. The digit "8" represents the base itself, which triggers a carry-over to the next position, similar to how "10" works in decimal. Entering 8 or 9 in an octal field causes a parsing error because those values cannot exist in that specific radix.

Fractional parts are converted by repeatedly multiplying the decimal fraction by the target base (e.g., 2). The integer part of the result becomes the next digit in the sequence. This process continues until the fraction reaches zero or the desired precision is met. Be aware that some simple decimal fractions (like 0.1) result in repeating infinite sequences in binary.

This tool utilizes a BigInt-compatible custom implementation for integer parts, allowing for numbers far exceeding standard 64-bit limits. However, fractional precision is limited by standard floating-point arithmetic (IEEE 754), which maintains accuracy up to approximately 15-17 significant decimal digits.

Base-36 is often used to compress large numbers into short alphanumeric strings, such as in URL shortening services or creating compact serial numbers. It utilizes digits 0-9 and letters A-Z.