Write a C++ Program to Convert Binary Number to Octal and vice-versa

write-a-c++-program-to-convert-binary-number-to-octal-and-vice-versa

In this post, we will learn how to convert binary numbers to octal numbers and vice versa using C++ programming language.

Binary to Octal Conversion

To convert a binary number to an octal number, we need to first convert the binary number to a decimal number and then convert the decimal number to an octal number.

To convert a binary number to a decimal number, we can use the following algorithm:

  1. Initialize the decimal number to zero.
  2. Multiply the rightmost digit of the binary number by 2^0, the next digit by 2^1, and so on.
  3. Add the products obtained in step 2 to get the decimal equivalent.

For example, consider the binary number 101101. To convert it to a decimal number, we use the following algorithm:

decimal = 1(2^5) + 0(2^4) + 1(2^3) + 1(2^2) + 0(2^1) + 1(2^0) = 45

Now, to convert the decimal number 45 to an octal number, we can use the following algorithm:

  1. Divide the decimal number by 8 and store the remainder.
  2. Repeat step 1 until the quotient becomes zero.
  3. The octal equivalent is obtained by writing the remainders in reverse order.

For example, to convert the decimal number 45 to an octal number, we use the following algorithm:

45/8 = 5 remainder 5
5/8 = 0 remainder 5

Therefore, the octal equivalent of 45 is 55.

Here’s the C++ code to implement the above algorithm:

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    long long binary, decimal = 0;
    int octal = 0, i = 0;

    cout << "Enter a binary number: ";
    cin >> binary;

    // Convert binary to decimal
    while(binary != 0) {
        decimal += (binary % 10) * pow(2, i);
        ++i;
        binary /= 10;
    }

    i = 1;

    // Convert decimal to octal
    while (decimal != 0) {
        octal += (decimal % 8) * i;
        decimal /= 8;
        i *= 10;
    }

    cout << "The octal equivalent is " << octal << endl;
    return 0;
}

Binary to Octal Conversion

To convert an octal number to a binary number, we need to convert each octal digit to a 3-bit binary number.

For example, consider the octal number 74. To convert it to a binary number, we use the following algorithm:

7 = 111 (in binary)
4 = 100 (in binary)

Therefore, the binary equivalent of 74 is 111100.

Here’s the C++ code to implement the above algorithm:

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    int octal, decimal = 0, i = 0;
    long long binary = 0;

    cout << "Enter an octal number: ";
    cin >> octal;

    // Convert octal to decimal
    while(octal != 0) {
        decimal += (octal % 10) * pow(8, i);
        ++i;
        octal /= 10;
    }

    i = 1;

    // Convert decimal to binary
    while (decimal != 0) {
        binary += (decimal % 2) * i;
        decimal /= 2;
    i *= 10;
}

cout << "The binary equivalent is " << binary << endl;
return 0;
}

In conclusion, we have learned how to convert binary numbers to octal numbers and vice versa using C++ programming language.

The conversion process involves converting a binary number to a decimal number and then converting the decimal number to an octal number or converting an octal number to a binary number by converting each octal digit to a 3-bit binary number.

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