Number System Conversion

Number system conversion is the process of converting a number from one base to another. The most common number systems are:

Binary (Base 2): Uses only two digits, 0 and 1
Octal (Base 8): Uses digits from 0 to 7
Decimal (Base 10): Uses digits from 0 to 9
Hexadecimal (Base 16): Uses digits from 0 to 9 and letters A to F

1. Binary to Decimal Conversion

Code:

binary-to-decimal.cpp

#include <iostream>
 
using namespace std;
 
int main()
{
    int n;
 
    cout << "Enter a binary no: ";
    cin >> n;
 
    int ans = 0;
    int mul = 1;
    int on = n;
 
    while (n != 0)
    {
        int rem = n % 10;
        if (rem != 0 && rem != 1)
        {
            cout << "Invalid binary no." << endl;
            return 0;
        }
        n /= 10;
 
        ans += rem * mul;
        mul *= 2;
    }
 
    cout << "Decimal no. of " << on << " : " << ans << endl;
 
    return 0;
}

Output:

Enter a binary no: 111 Decimal no. of 111 : 7

2. Octal to Decimal Conversion

Code:

octal-to-decimal.cpp

#include <iostream>
 
using namespace std;
 
int main()
{
    int n;
 
    cout << "Enter an octal no: ";
    cin >> n;
 
    int ans = 0;
    int mul = 1;
    int on = n;
 
    while (n != 0)
    {
        int rem = n % 10;
        if (rem < 0 || rem > 7)
        {
            cout << "Invalid octal no." << endl;
            return 0;
        }
        n /= 10;
 
        ans += rem * mul;
        mul *= 8;
    }
 
    cout << "Decimal no. of " << on << " : " << ans << endl;
 
    return 0;
}

Output:

Enter a octal no: 173 Decimal no. of 173 : 123

3. Decimal to Binary Conversion

Code:

decimal-to-binary.cpp

#include <iostream>
 
using namespace std;
 
int main()
{
    int n;
 
    cout << "Enter a no: ";
    cin >> n;
 
    int ans = 0;
    int mul = 1;
    int on = n;
 
    while (n != 0)
    {
        int rem = n % 2;
        n /= 2;
 
        ans += rem * mul;
        mul *= 10;
    }
 
    cout << "Binary no. of " << on << " : " << ans << endl;
 
    return 0;
}

Output:

Enter a no: 7 Binary no. of 7 : 111

4. Decimal to Octal Conversion

Code:

decimal-to-octal.cpp

#include <iostream>
 
using namespace std;
 
int main()
{
    int n;
 
    cout << "Enter a no: ";
    cin >> n;
 
    int ans = 0;
    int mul = 1;
    int on = n;
 
    while (n != 0)
    {
        int rem = n % 8;
        n /= 8;
 
        ans += rem * mul;
        mul *= 10;
    }
 
    cout << "Octal no. of " << on << " : " << ans << endl;
 
    return 0;
}

Output:

Enter a no: 123 Octal no. of 123 : 173