Convert Octal to Decimal in C++

This program teaches you how to convert an octal number to its decimal (base-10) equivalent in C++. Octal is a base-8 number system that uses digits 0-7. While less common than binary or decimal, octal is still used in some computing contexts, especially for file permissions in Unix/Linux systems. Understanding octal conversion helps you work with different number systems.

What This Program Does

The program converts an octal number (base-8) to a decimal number (base-10). For example:

Input octal: 12
Output decimal: 10

Octal numbers use digits 0-7, while decimal numbers use digits 0-9. The conversion involves multiplying each octal digit by 8 raised to its position power and summing the results.

Example:

12 (octal) = 1×8¹ + 2×8⁰ = 8 + 2 = 10 (decimal)
145 (octal) = 1×8² + 4×8¹ + 5×8⁰ = 64 + 32 + 5 = 101 (decimal)

Algorithm

The conversion uses a while loop:

cpp
while (temp != 0) {
    remainder = temp % 10;
    temp /= 10;
    decimal += remainder * pow(8, i);
    ++i;
}

Step-by-step for octal = 12:

Extract rightmost digit: 12 % 10 = 2, decimal = 0 + 2×8⁰ = 2
Remove digit: 12 / 10 = 1
Extract digit: 1 % 10 = 1, decimal = 2 + 1×8¹ = 10
Final result: decimal = 10

Understanding Octal System

Positional Value System:

In octal, each position represents a power of 8:

Position 0 (rightmost): 8⁰ = 1
Position 1: 8¹ = 8
Position 2: 8² = 64
Position 3: 8³ = 512

Valid Octal Digits:

Octal uses only digits 0, 1, 2, 3, 4, 5, 6, 7
Digits 8 and 9 are not valid in octal

Why Octal?:

Historically used in computing (easier to read than binary)
Still used for file permissions in Unix/Linux (e.g., chmod 755)
Groups of 3 binary digits correspond to 1 octal digit

Summary

Octal-to-decimal conversion multiplies each digit by 8^position and sums the results.
Octal is base-8 (uses digits 0-7), decimal is base-10 (uses digits 0-9).
The algorithm processes digits from right to left (least significant to most significant).
Understanding octal is useful for file permissions and system administration.

This program is essential for understanding number systems, file permissions, and system administration tasks.

Output