Convert the given BCD to its equivalent Binary form

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

Examples:

Input: 1001000
Output: 110000
Explanation:
Integer value of the given BCD is 48(0100 -> 4, 1000 -> 8).
(48)10 = (110000)2



Input: 1001001
Output: 110001

Approach: In order to solve this problem we need to split the given BCD number into binary chunks of length 4 and convert them to integer one by one to generate the final integer representation of the given BCD. Once generated, convert the integer to its binary form.

Below is the implementation of the above approach.

C++

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// C++ code to convert BCD to its
// equivalent Binary
  
#include <bits/stdc++.h>
using namespace std;
  
// Function to convert BCD to Decimal
string bcdToBinary(string s)
{
    int l = s.length();
    int num = 0;
    int mul = 1;
    int sum = 0;
    // If the length of given BCD is not
    // divisible by 4
    for (int i = l % 4 - 1; i >= 0; i--) {
        sum += (s[i] - '0') * mul;
        mul *= 2;
    }
  
    num = sum;
  
    sum = 0;
    mul = pow(2, 3);
    int ctr = 0;
    for (int i = l % 4; i < l; i++) {
        ctr++;
        sum += (s[i] - '0') * mul;
        mul /= 2;
        if (ctr == 4) {
            num = num * 10 + sum;
            sum = 0;
            mul = pow(2, 3);
            ctr = 0;
        }
    }
  
    // Convert decimal to binary
    string ans = "";
    while (num > 0) {
        ans += (char)(num % 2 + '0');
        num /= 2;
    }
  
    reverse(ans.begin(), ans.end());
  
    return ans;
}
  
// Driver Code
int main()
{
    string s = "1001000";
  
    // Function Call
    cout << bcdToBinary(s);
  
    return 0;
}

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Output:

110000

Time Complexity: O(N) where N denotes the length of the BCD string provided
Auxiliary Space: O(1)

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