About

Octal notation (base-8) remains a staple in Unix-based file systems for defining permissions (chmod) and in legacy computing architectures where 12-bit, 24-bit, or 36-bit words were common. Unlike hexadecimal, which groups bits by four, octal groups bits by three. This tool handles the conversion of standard base-10 decimals into octal representation.

Accuracy is paramount when dealing with fractional octal values in low-level signal processing or specific floating-point encoding schemes. This utility calculates the integer part via repeated division and the fractional part via repeated multiplication, ensuring precision up to 8 octal places. It is designed for systems engineers, Linux administrators, and computer science students requiring immediate verification of manual calculations.

Formulas

The conversion is split into two parts: integer and fractional.

1. Integer Part (Repeated Division):

N = q × 8 + r

Where q is the quotient and r is the remainder. The octal digits are the remainders read in reverse order.

2. Fractional Part (Repeated Multiplication):

F × 8 = I + F_new

We take the integer part I as the next octal digit and repeat with the new fractional part F_new.

Reference Data

Decimal (Base-10)	Octal (Base-8)	Binary (3-bit)	Typical Usage (chmod)
0	0	000	No Permission
1	1	001	Execute
2	2	010	Write
3	3	011	Write + Execute
4	4	100	Read
5	5	101	Read + Execute
6	6	110	Read + Write
7	7	111	Read + Write + Execute
8	10	001 000	-
10	12	001 010	-
15	17	001 111	-
16	20	010 000	-
64	100	001 000 000	-
255	377	011 111 111	Byte Limit

Frequently Asked Questions

Fractional conversion from base-10 to base-8 can result in repeating decimals (non-terminating expansions). We limit the precision to 8 places to prevent infinite loops and provide a usable approximation for computing contexts.

This tool calculates the absolute value conversion and prepends a negative sign. In computing, negative numbers are typically represented using two"s complement, which requires a fixed bit-width context not assumed here.

The tool utilizes standard floating-point precision. However, for integers larger than 2^53 - 1 (safe integer limit), precision loss may occur in the input stage itself.

Linux permissions use a 3-digit octal code (e.g., 755). Each digit represents the sum of Read (4), Write (2), and Execute (1) permissions for User, Group, and Others respectively.