Program to Convert BCD number into Decimal number

Given a BCD (Binary Coded Decimal) number, the task is to convert the BCD number into its equivalent Decimal number. 

Examples:

Input: BCD = 100000101000 
Output: 828 
Explanation:
Dividing the number into chunks of 4, it becomes 1000 0010 1000. 
Here, 1000 is equivalent to 8 and 
0010 is equivalent to 2. 
So, the number becomes 828.

Input: BCD = 1001000 
Output: 48 
Explanation:
Dividing the number into chunks of 4, it becomes 0100 1000. 
Here, 0100 is equivalent to 4 and 
1000 is equivalent to 8. 
So, the number becomes 48.  

Approach:

1. Iterate over all bits in given BCD numbers.
2. Divide the given BCD number into chunks of 4, and start computing its equivalent Decimal number. 
3. Store this number formed in a variable named sum. 
4. Start framing a number from the digits stored in the sum in a variable num. 
5. Reverse the number formed so far and return that number. 
   

Below is the implementation of the above approach.  

C++

// C++ code to convert BCD to its
// decimal number(base 10).

// Including Header Files
#include <bits/stdc++.h>
using namespace std;

// Function to convert BCD to Decimal
int bcdToDecimal(string s)
{
    int len = s.length(),
        check = 0, check0 = 0;
    int num = 0, sum = 0,
        mul = 1, rev = 0;

    // Iterating through the bits backwards
    for (int i = len - 1; i >= 0; i--) {

        // Forming the equivalent
        // digit(0 to 9)
        // from the group of 4.
        sum += (s[i] - '0') * mul;
        mul *= 2;
        check++;

        // Reinitialize all variables
        // and compute the number.
        if (check == 4 || i == 0) {
            if (sum == 0 && check0 == 0) {
                num = 1;
                check0 = 1;
            }
            else {
                // update the answer
                num = num * 10 + sum;
            }

            check = 0;
            sum = 0;
            mul = 1;
        }
    }

    // Reverse the number formed.
    while (num > 0) {
        rev = rev * 10 + (num % 10);
        num /= 10;
    }

    if (check0 == 1)
        return rev - 1;

    return rev;
}

// Driver Code
int main()
{
    string s = "100000101000";

    // Function Call
    cout << bcdToDecimal(s);

    return 0;
}

Java

// Java code to convert BCD to its
// decimal number(base 10).
// Including Header Files
import java.io.*;
import java.util.*;

class GFG {

// Function to convert BCD to Decimal
public static int bcdToDecimal(String s)
{
    int len = s.length();
    int check = 0, check0 = 0;
    int num = 0, sum = 0;
    int mul = 1, rev = 0;

    // Iterating through the bits backwards
    for(int i = len - 1; i >= 0; i--)
    {

       // Forming the equivalent
       // digit(0 to 9)
       // from the group of 4.
       sum += (s.charAt(i) - '0') * mul;
       mul *= 2;
       check++;

       // Reinitialize all variables
       // and compute the number.
       if (check == 4 || i == 0)
       {
           if (sum == 0 && check0 == 0)
           {
               num = 1;
               check0 = 1;
           }
           else
           {

               // Update the answer
               num = num * 10 + sum;
           }

           check = 0;
           sum = 0;
           mul = 1;
       }
    }

    // Reverse the number formed.
    while (num > 0)
    {
        rev = rev * 10 + (num % 10);
        num /= 10;
    }

    if (check0 == 1)
        return rev - 1;

    return rev;
}

// Driver code
public static void main(String[] args)
{
    String s = "100000101000";

    // Function Call
    System.out.println(bcdToDecimal(s));
}
}

// This code is contributed by coder001

Python3

# Python3 code to convert BCD to its
# decimal number(base 10).

# Function to convert BCD to Decimal
def bcdToDecimal(s):

    length = len(s);
    check = 0;
    check0 = 0;
    num = 0;
    sum = 0;
    mul = 1;
    rev = 0;

    # Iterating through the bits backwards
    for i in range(length - 1, -1, -1):

        # Forming the equivalent
        # digit(0 to 9)
        # from the group of 4.
        sum += (ord(s[i]) - ord('0')) * mul;
        mul *= 2;
        check += 1;

        # Reinitialize all variables
        # and compute the number
        if (check == 4 or i == 0):
            if (sum == 0 and check0 == 0):
                num = 1;
                check0 = 1;

            else:

                # Update the answer
                num = num * 10 + sum;

            check = 0;
            sum = 0;
            mul = 1;

    # Reverse the number formed.
    while (num > 0):
        rev = rev * 10 + (num % 10);
        num //= 10;

    if (check0 == 1):
        return rev - 1;

    return rev;

# Driver Code
if __name__ == "__main__":

    s = "100000101000";

    # Function Call
    print(bcdToDecimal(s));

# This code is contributed by AnkitRai01

C#

// C# code to convert BCD to its
// decimal number(base 10).
// Including Header Files
using System;

class GFG
{

// Function to convert BCD to Decimal
public static int bcdToDecimal(String s)
{
    int len = s.Length;
    int check = 0, check0 = 0;
    int num = 0, sum = 0;
    int mul = 1, rev = 0;

    // Iterating through the bits backwards
    for(int i = len - 1; i >= 0; i--)
    {

        // Forming the equivalent
        // digit(0 to 9)
        // from the group of 4.
        sum += (s[i] - '0') * mul;
        mul *= 2;
        check++;

        // Reinitialize all variables
        // and compute the number.
        if (check == 4 || i == 0)
        {
            if (sum == 0 && check0 == 0)
            {
                num = 1;
                check0 = 1;
            }
            else
            {

                // Update the answer
                num = num * 10 + sum;
            }

            check = 0;
            sum = 0;
            mul = 1;
        }
    }

    // Reverse the number formed.
    while (num > 0)
    {
        rev = rev * 10 + (num % 10);
        num /= 10;
    }

    if (check0 == 1)
        return rev - 1;

    return rev;
}

// Driver code
public static void Main(String[] args)
{
    String s = "100000101000";

    // Function Call
    Console.WriteLine(bcdToDecimal(s));
}
}

// This code is contributed by 29AjayKumar

Javascript

<script>

// Javascript code to convert BCD to its
// decimal number(base 10).
// Including Header Files

// Function to convert BCD to Decimal
function bcdToDecimal(s)
{
    let len = s.length;
    let check = 0, check0 = 0;
    let num = 0, sum = 0;
    let mul = 1, rev = 0;

    // Iterating through the bits backwards
    for(let i = len - 1; i >= 0; i--)
    {

       // Forming the equivalent
       // digit(0 to 9)
       // from the group of 4.
       sum += (s[i] - '0') * mul;
       mul *= 2;
       check++;

       // Reinitialize all variables
       // and compute the number.
       if (check == 4 || i == 0)
       {
           if (sum == 0 && check0 == 0)
           {
               num = 1;
               check0 = 1;
           }
           else
           {

               // Update the answer
               num = num * 10 + sum;
           }

           check = 0;
           sum = 0;
           mul = 1;
       }
    }

    // Reverse the number formed.
    while (num > 0)
    {
        rev = rev * 10 + (num % 10);
        num = Math.floor(num / 10);
    }

    if (check0 == 1)
        return rev - 1;

    return rev;
}

// Driver Code

    let s = "100000101000";

    // Function Call
    document.write(bcdToDecimal(s.split('')));

</script>

Output:

828

Time complexity: O(N) 
Auxiliary Space complexity: O(1) 

Method: Using bit manipulation method

The bcdToDecimal function takes a string s representing the BCD number as input and returns its decimal equivalent. It first initializes the num variable to 0. Then, it iterates through the bits of the BCD string in groups of 4, using the substr function to extract each group. For each group, it creates a bitset object with the 4 bits, and converts it to decimal using the to_ulong function. It then multiplies the decimal value by the appropriate place value and adds it to the num variable. Finally, the function returns num.

C++

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

// Function to convert BCD to Decimal
int bcdToDecimal(string s)
{
    int len = s.length(), num = 0;

    // Iterating through the bits
    for (int i = 0; i < len; i+=4) {

        // Extracting the 4 bits from the BCD string
        bitset<4> bcd_bits(s.substr(i, 4));

        // Converting the 4 bits to decimal
        int dec = bcd_bits.to_ulong();

        // Multiplying by the place value and adding to the result
        num = num*10 + dec;
    }

    return num;
}

// Driver Code
int main()
{
    string s = "100000101000";

    // Function Call
    cout << bcdToDecimal(s);

    return 0;
}

Output

828

The time complexity of this algorithm is O(n), where n is the length of the BCD string. This is because the algorithm must iterate through each bit of the string once. 

The auxiliary space complexity is also O(n), because the bitset objects created in each iteration require O(1) space, but there are n/4 iterations.