# Program to Convert BCD number into Decimal number

Last Updated : 20 Sep, 2023

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 ` `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

 ``

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 ` `#include ` `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;` `}`

## Java

 `public` `class` `BCDToDecimal {` `    ``// Function to convert a binary-coded decimal (BCD) ` `  ``// string to its decimal representation` `    ``public` `static` `int` `bcdToDecimal(String s) {` `        ``int` `len = s.length();` `        ``int` `num = ``0``;`   `        ``// Iterate through the BCD string, reading 4 bits at a time` `        ``for` `(``int` `i = ``0``; i < len; i += ``4``) {` `            ``// Extract the 4-bit BCD representation` `            ``String bcdBits = s.substring(i, i + ``4``);`   `            ``// Convert the BCD representation to its decimal value ` `          ``// using Integer.parseInt` `            ``int` `dec = Integer.parseInt(bcdBits, ``2``);`   `            ``// Append the decimal value to the result number` `            ``num = num * ``10` `+ dec;` `        ``}`   `        ``// Return the final decimal number` `        ``return` `num;` `    ``}`   `    ``public` `static` `void` `main(String[] args) {` `        ``String s = ``"100000101000"``;` `        ``System.out.println(bcdToDecimal(s));` `    ``}` `}`

## Python3

 `def` `bcd_to_decimal(s):` `    ``num ``=` `0` `    ``len_s ``=` `len``(s)` `    `  `    ``for` `i ``in` `range``(``0``, len_s, ``4``):` `        ``# Extracting the 4 bits from the BCD string` `        ``bcd_bits ``=` `s[i:i``+``4``]`   `        ``# Converting the 4 bits to decimal` `        ``dec ``=` `int``(bcd_bits, ``2``)`   `        ``# Multiplying by the place value and adding to the result` `        ``num ``=` `num ``*` `10` `+` `dec`   `    ``return` `num`   `# Driver code` `s ``=` `"100000101000"`   `# Function call` `print``(bcd_to_decimal(s))`

## C#

 `using` `System;`   `public` `class` `GFG` `{` `    ``// Function to convert BCD to Decimal` `    ``public` `static` `int` `BcdToDecimal(``string` `s)` `    ``{` `        ``int` `len = s.Length;` `        ``int` `num = 0;` `        `  `        ``// Iterating through the bits` `        ``for` `(``int` `i = 0; i < len; i += 4)` `        ``{` `            ``// Extracting the 4 bits from the BCD string` `            ``string` `bcdSubstring = s.Substring(i, 4);` `            `  `            ``// Parsing the 4 bits as a binary number` `            ``int` `dec = Convert.ToInt32(bcdSubstring, 2);` `            `  `            ``// Multiplying by the place value and adding to the result` `            ``num = num * 10 + dec;` `        ``}`   `        ``return` `num;` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `Main()` `    ``{` `        ``string` `s = ``"100000101000"``;`   `        ``// Function Call` `        ``Console.WriteLine(BcdToDecimal(s));` `    ``}` `}`

## Javascript

 `function` `bcdToDecimal(s) {` `    ``const len = s.length;` `    ``let num = 0;`   `    ``// Iterating through the bits` `    ``for` `(let i = 0; i < len; i += 4) {` `        ``// Extracting the 4 bits from the BCD string` `        ``const bcdSubstring = s.substring(i, i + 4);`   `        ``// Parsing the 4 bits as a binary number` `        ``const dec = parseInt(bcdSubstring, 2);`   `        ``// Multiplying by the place value and adding to the result` `        ``num = num * 10 + dec;` `    ``}`   `    ``return` `num;` `}`   `// Driver Code` `const s = ``"100000101000"``;`   `// Function Call` `console.log(bcdToDecimal(s));`

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.

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