Master octal to decimal conversion with our comprehensive online calculator. Learn how to convert decimal to octal and octal to decimal using step-by-step methods, conversion formulas, and real-world examples. Perfect for programming, Unix permissions, and computer science education.
Professional octal to decimal converter supporting bidirectional conversion with instant results. Features detailed conversion explanations, Unix permission calculator, programming examples in Python/Java/C++, and practice problems including 5267 octal to decimal, 1743 octal conversions, and more.
The fundamental principle behind octal to decimal conversion lies in understanding the base-8 positional number system. Each digit position represents a power of 8, starting from 8⁰ = 1 for the rightmost digit. This systematic approach makes octal to decimal conversion straightforward and accurate for any size number.
Octal (base-8) uses digits 0-7, where each position represents increasing powers of 8. This positional value system allows us to convert any octal number to its decimal equivalent by calculating the weighted sum of each digit multiplied by its corresponding power of 8.
Result: 755₈ = 493₁₀ (Unix permission: rwxr-xr-x)
This demonstrates how to convert larger octal numbers to decimal
Answer: 1743₈ = 995₁₀ (Common octal conversion practice)
Essential powers of 8 for manual octal to decimal conversion calculations.
This division method demonstrates how to convert decimal to octal by repeatedly dividing by 8 and collecting remainders. The process is the reverse of octal to decimal conversion, making it essential for bidirectional number system conversions.
| Octal | Decimal | Binary |
|---|---|---|
| 0 | 0 | 000 |
| 1 | 1 | 001 |
| 2 | 2 | 010 |
| 3 | 3 | 011 |
| 4 | 4 | 100 |
| 5 | 5 | 101 |
| 6 | 6 | 110 |
| 7 | 7 | 111 |
| Octal | Decimal | Unix Permission |
|---|---|---|
| 644 | 420 | rw-r--r-- |
| 755 | 493 | rwxr-xr-x |
| 777 | 511 | rwxrwxrwx |
| 600 | 384 | rw------- |
| 700 | 448 | rwx------ |
| 666 | 438 | rw-rw-rw- |
| 555 | 365 | r-xr-xr-x |
| 444 | 292 | r--r--r-- |
| 10 | 8 | --------x |
| 77 | 63 | --rwxrwx |
Each permission digit is the sum of: Read (4) + Write (2) + Execute (1). For example, 7 = 4+2+1 (full permissions), 5 = 4+1 (read + execute), 4 = read only.
Learn how to implement octal to decimal conversion in major programming languages. These examples demonstrate both built-in functions and manual conversion methods for educational purposes.
# Complete Python octal to decimal converter
def octal_to_decimal(octal_str):
"""Convert octal string to decimal integer"""
try:
decimal = int(octal_str, 8)
return decimal
except ValueError:
return "Invalid octal number"
# Example: Convert 5267 octal to decimal
result = octal_to_decimal("5267")
print(f"5267₈ = {result}₁₀") # Output: 5267₈ = 2743₁₀
# How to use octal and decimal in Python
def decimal_to_octal(decimal_num):
"""Convert decimal to octal"""
return oct(decimal_num)[2:] # Remove '0o' prefix
# Bidirectional conversion examples
octal_nums = ["755", "1743", "644", "777"]
for octal in octal_nums:
decimal = octal_to_decimal(octal)
back_to_octal = decimal_to_octal(decimal)
print(f"{octal}₈ → {decimal}₁₀ → {back_to_octal}₈")
# Unix permissions with octal
import stat
permissions = [0o755, 0o644, 0o777, 0o600]
for perm in permissions:
print(f"{oct(perm)} = {stat.filemode(perm)}")
// Octal to Decimal
const octalStr = "755";
const decimal = parseInt(octalStr, 8);
console.log(`Octal ${octalStr} = Decimal ${decimal}`);
// Output: Octal 755 = Decimal 493
// Decimal to Octal
const dec = 493;
const octal = dec.toString(8);
console.log(`Decimal ${dec} = Octal ${octal}`);
// Output: Decimal 493 = Octal 755
// Permission parser
function parseOctalPerm(octal) {
const perms = ['---', '--x', '-w-', '-wx',
'r--', 'r-x', 'rw-', 'rwx'];
return octal.split('').map(d => perms[d]).join('');
}// Octal to Decimal
String octalStr = "755";
int decimal = Integer.parseInt(octalStr, 8);
System.out.println("Octal " + octalStr +
" = Decimal " + decimal);
// Output: Octal 755 = Decimal 493
// Decimal to Octal
int dec = 493;
String octal = Integer.toOctalString(dec);
System.out.println("Decimal " + dec +
" = Octal " + octal);
// Output: Decimal 493 = Octal 755
// Using octal literals
int permission = 0755; // Octal literal
System.out.println("Permission: " + permission);#include <iostream>
#include <string>
using namespace std;
// Octal to Decimal
string octal = "755";
int decimal = stoi(octal, 0, 8);
cout << "Octal " << octal << " = Decimal "
<< decimal << endl;
// Output: Octal 755 = Decimal 493
// Decimal to Octal using iostream
int dec = 493;
cout << "Decimal " << dec << " = Octal "
<< oct << dec << endl;
// Output: Decimal 493 = Octal 755
// File permissions in Unix systems
#include <sys/stat.h>
chmod("file.txt", 0755); // Set permissionsThe easiest way to convert octal to decimal is using the positional notation method: multiply each octal digit by 8 raised to its position power (starting from 0 on the right), then sum all results. For example, 755₈ = 7×8² + 5×8¹ + 5×8⁰ = 448 + 40 + 5 = 493₁₀.
To convert 5267 octal to decimal: 5×8³ + 2×8² + 6×8¹ + 7×8⁰ = 5×512 + 2×64 + 6×8 + 7×1 = 2560 + 128 + 48 + 7 = 2743₁₀. This demonstrates the systematic approach for converting any octal number to decimal.
Most programming languages provide built-in functions: Python uses int("755", 8), JavaScript uses parseInt("755", 8), Java uses Integer.parseInt("755", 8), and C++ uses stoi("755", 0, 8). These functions automatically handle the octal to decimal conversion using the base-8 interpretation.
Unix permissions use octal because each permission group (owner, group, others) uses exactly 3 bits (read=4, write=2, execute=1). Since 3 bits can represent values 0-7, octal notation perfectly matches this structure. For example, 755₈ means owner has rwx (7), group has r-x (5), others have r-x (5).
Octal (base-8) uses digits 0-7, decimal (base-10) uses digits 0-9, and hexadecimal (base-16) uses digits 0-9 and letters A-F. Each system represents numbers differently: 100₈ = 64₁₀ = 40₁₆. Understanding these conversions is essential for computer programming and system administration.
Practice decimal to octal practice questions by using the division method: repeatedly divide by 8 and collect remainders. Start with simple numbers like 64₁₀ = 100₈, then progress to complex examples like 918₁₀ = 1626₈. Verify your answers by converting back using octal to decimal methods.