Write a program to add two numbers in base 14

Asked by Anshya.

Base 14:

Decimal numbers	Base 14 numbers
0	0
1	1
2	2
3	3
4	4
5	5
6	6
7	7
8	8
9	9
10	A
11	B
12	C
13	D
14	D1

Below are the different ways to add base 14 numbers.
Method 1
Thanks to Raj for suggesting this method. 

  1. Convert both i/p base 14 numbers to base 10.
  2. Add numbers.
  3. Convert the result back to base 14.

Method 2
Just add the numbers in base 14 in the same way we add in base 10. Add numerals of both numbers one by one from right to left. If there is a carry while adding two numerals, consider the carry for adding the next numerals.
Let us consider the presentation of base 14 numbers same as hexadecimal numbers  

   A --> 10
   B --> 11
   C --> 12
   D --> 13

Example:
   num1 =       1  2  A
   num2 =       C  D  3   

   1. Add A and 3, we get 13(D). Since 13 is smaller than 
14, carry becomes 0 and resultant numeral becomes D         

  2. Add 2, D and carry(0). we get 15. Since 15 is greater 
than 13, carry becomes 1 and resultant numeral is 15 - 14 = 1

  3. Add 1, C and carry(1). we get 14. Since 14 is greater 
than 13, carry becomes 1 and resultant numeral is 14 - 14 = 0

Finally, there is a carry, so 1 is added as leftmost numeral and the result becomes 
101D 

Implementation of Method 2

C++

#include <bits/stdc++.h>
using namespace std;
# define bool int

int getNumeralValue(char );
char getNumeral(int );

/* Function to add two numbers in base 14 */
char *sumBase14(char num1[], char num2[])
{
    int l1 = strlen(num1);
    int l2 = strlen(num2);
    char *res;
    int i;
    int nml1, nml2, res_nml;
    bool carry = 0;

    if(l1 != l2)
    {
        cout << "Function doesn't support numbers of different"
                " lengths. If you want to add such numbers then"
                " prefix smaller number with required no. of zeroes";
        assert(0);
    }

    /* Note the size of the allocated memory is one
        more than i/p lengths for the cases where we
        have carry at the last like adding D1 and A1 */
    res = new char[(sizeof(char)*(l1 + 1))];

    /* Add all numerals from right to left */
    for(i = l1-1; i >= 0; i--)
    {
        /* Get decimal values of the numerals of
        i/p numbers*/
        nml1 = getNumeralValue(num1[i]);
        nml2 = getNumeralValue(num2[i]);

        /* Add decimal values of numerals and carry */
        res_nml = carry + nml1 + nml2;

        /* Check if we have carry for next addition
            of numerals */
        if(res_nml >= 14)
        {
            carry = 1;
            res_nml -= 14;
        }
        else
        {
               carry = 0;
        }
        res[i+1] = getNumeral(res_nml);
    }

    /* if there is no carry after last iteration
        then result should not include 0th character
        of the resultant string */
    if(carry == 0)
        return (res + 1);

    /* if we have carry after last iteration then
        result should include 0th character */
    res[0] = '1';
    return res;
}

/* Function to get value of a numeral
For example it returns 10 for input 'A'
1 for '1', etc */
int getNumeralValue(char num)
{
    if( num >= '0' && num <= '9')
        return (num - '0');
    if( num >= 'A' && num <= 'D')
        return (num - 'A' + 10);

    /* If we reach this line caller is giving
        invalid character so we assert and fail*/
    assert(0);
}

/* Function to get numeral for a value.
For example it returns 'A' for input 10
'1' for 1, etc */
char getNumeral(int val)
{
    if( val >= 0 && val <= 9)
        return (val + '0');
    if( val >= 10 && val <= 14)
        return (val + 'A' - 10);

    /* If we reach this line caller is giving
        invalid no. so we assert and fail*/
    assert(0);
}

/*Driver code*/
int main()
{
    char num1[] = "DC2";
    char num2[] = "0A3";

    cout<<"Result is "<<sumBase14(num1, num2);
    return 0;
}

// This code is contributed by rathbhupendra

C

# include <stdio.h>
# include <stdlib.h>
# define bool int

int getNumeralValue(char );
char getNumeral(int );

/* Function to add two numbers in base 14 */
char *sumBase14(char *num1,  char *num2)
{
   int l1 = strlen(num1);
   int l2 = strlen(num2);
   char *res;
   int i;
   int nml1, nml2, res_nml;
   bool carry = 0;

   if(l1 != l2)
   {
     printf("Function doesn't support numbers of different"
            " lengths. If you want to add such numbers then"
            " prefix smaller number with required no. of zeroes");
     getchar();
     assert(0);
   }

   /* Note the size of the allocated memory is one
     more than i/p lengths for the cases where we
     have carry at the last like adding D1 and A1 */
   res = (char *)malloc(sizeof(char)*(l1 + 1));

   /* Add all numerals from right to left */
   for(i = l1-1; i >= 0; i--)
   {
     /* Get decimal values of the numerals of
       i/p numbers*/
     nml1 = getNumeralValue(num1[i]);
     nml2 = getNumeralValue(num2[i]);

     /* Add decimal values of numerals and carry */
     res_nml = carry + nml1 + nml2;

     /* Check if we have carry for next addition
        of numerals */
     if(res_nml >= 14)
     {
       carry = 1;
       res_nml -= 14;
     }
     else
     {
       carry = 0;
     }
     res[i+1] = getNumeral(res_nml);
   }

   /* if there is no carry after last iteration
      then result should not include 0th character
      of the resultant string */
   if(carry == 0)
     return (res + 1);

   /* if we have carry after last iteration then
     result should include 0th character */
   res[0] = '1';
   return res;
}

/* Function to get value of a numeral
  For example it returns 10 for input 'A'
  1 for '1', etc */
int getNumeralValue(char num)
{
  if( num >= '0' && num <= '9')
    return (num - '0');
  if( num >= 'A' && num <= 'D')
    return (num - 'A' + 10);

  /* If we reach this line caller is giving
    invalid character so we assert and fail*/
  assert(0);
}

/* Function to get numeral for a value.
  For example it returns 'A' for input 10
  '1' for 1, etc */
char getNumeral(int val)
{
  if( val >= 0 && val <= 9)
    return (val + '0');
  if( val >= 10 && val <= 14)
    return (val + 'A' - 10);

  /* If we reach this line caller is giving
    invalid no. so we assert and fail*/
  assert(0);
}

/*Driver program to test above functions*/
int main()
{
    char *num1 = "DC2";
    char *num2 = "0A3";

    printf("Result is %s", sumBase14(num1, num2));
    getchar();
    return 0;
}

Java

// Java program for the
// above approach
import java.util.*;
class GFG{

// Function to add two
// numbers in base 14
static String sumBase14(char num1[],
                        char num2[])
{
  int l1 = num1.length;
  int l2 = num2.length;
  char []res;
  int i;
  int nml1, nml2, res_nml;
  int carry = 0;

  if(l1 != l2)
  {
    System.out.print("Function doesn't support " +
                     "numbers of different " +
                     "lengths. If you want to " +
                     "dd such numbers then " +
                     "prefix smaller number " +
                     "with required no. of zeroes");
  }

  // Note the size of the allocated
  // memory is one more than i/p
  // lengths for the cases where we
  // have carry at the last like
  // adding D1 and A1
  res = new char[(4 * (l1 + 1))];

  // Add all numerals from
  // right to left
  for(i = l1 - 1; i >= 0; i--)
  {
    // Get decimal values of the
    // numerals of i/p numbers
    nml1 = getNumeralValue(num1[i]);
    nml2 = getNumeralValue(num2[i]);

    // Add decimal values of
    // numerals and carry
    res_nml = carry + nml1 + nml2;

    // Check if we have carry for
    // next addition of numerals
    if(res_nml >= 14)
    {
      carry = 1;
      res_nml -= 14;
    }
    else
    {
      carry = 0;
    }
    res[i + 1] = getNumeral(res_nml);
  }

  // If there is no carry after
  // last iteration then result
  // should not include 0th
  // character of the resultant
  // String
  if(carry == 0)
    return String.valueOf(res);

  // If we have carry after last
  // iteration then result should
  // include 0th character
  res[0] = '1';
  return String.valueOf(res);
}

// Function to get value of a numeral
// For example it returns 10 for input
// 'A' 1 for '1', etc
static int getNumeralValue(char num)
{
  if(num >= '0' && num <= '9')
    return (num - '0');
  if(num >= 'A' && num <= 'D')
    return (num - 'A' + 10);

  // If we reach this line
  // caller is giving invalid
  // character so we assert
  // and fail
  // assert(0);
  return 0;
}

// Function to get numeral
// for a value. For example
// it returns 'A' for input 10
// '1' for 1, etc
static char getNumeral(int val)
{
  if(val >= 0 && val <= 9)
    return (char)(val + '0');
  if(val >= 10 && val <= 14)
    return (char)(val + 'A' - 10);

  // If we reach this line
  // caller is giving invalid
  // no. so we assert and fail
  // assert(0);
  return '0';
}

// Driver code
public static void main(String[] args)
{
  char num1[] = {'D','C','2'};
  char num2[] = {'0','A','3'};
  System.out.print("Result is " +
                    sumBase14(num1,
                              num2));
}
}

// This code is contributed by 29AjayKumar

Python3

# Function to get value of a numeral
# For example it returns 10 for input 'A'
# 1 for '1', etc
def getNumeralValue(num) :

    if( num >= '0' and num <= '9') :
        return ord(num) - ord('0')
    if( num >= 'A' and num <= 'D') :
        return ord(num ) - ord('A') + 10

# Function to get numeral for a value.
# For example it returns 'A' for input 10
# '1' for 1, etc
def getNumeral(val):

    if( val >= 0 and val <= 9):
        return chr(val + ord('0'))
    if( val >= 10 and val <= 14) :
        return chr(val + ord('A') - 10)

# Function to add two numbers in base 14
def sumBase14(num1, num2):

    l1 = len(num1)
    l2 = len(num2)
    carry = 0

    if(l1 != l2) :

        print("Function doesn't support numbers of different"
                " lengths. If you want to add such numbers then"
                " prefix smaller number with required no. of zeroes")

    # Note the size of the allocated memory is one
    # more than i/p lengths for the cases where we
    # have carry at the last like adding D1 and A1
    res = [0]*(l1 + 1)

    # Add all numerals from right to left
    for i in range(l1 - 1, -1, -1):

        # Get decimal values of the numerals of
        # i/p numbers
        nml1 = getNumeralValue(num1[i])
        nml2 = getNumeralValue(num2[i])

        # Add decimal values of numerals and carry
        res_nml = carry + nml1 + nml2;

        # Check if we have carry for next addition
        # of numerals
        if(res_nml >= 14) :
            carry = 1
            res_nml -= 14
        else:
            carry = 0
        res[i+1] = getNumeral(res_nml)

    # if there is no carry after last iteration
    # then result should not include 0th character
    # of the resultant string
    if(carry == 0):
        return (res + 1)

    # if we have carry after last iteration then
    # result should include 0th character
    res[0] = '1'
    return res

# Driver code
if __name__ == "__main__":

    num1 = "DC2"
    num2 = "0A3"

    print("Result is ",end="")
    res = sumBase14(num1, num2)
    for i in range(len(res)):
        print(res[i],end="")

# This code is contributed by chitranayal

C#

// C# program for the
// above approach
using System;
class GFG{

// Function to add two
// numbers in base 14
static String sumBase14(char []num1,
                        char []num2)
{
  int l1 = num1.Length;
  int l2 = num2.Length;
  char []res;
  int i;
  int nml1, nml2, res_nml;
  int carry = 0;

  if(l1 != l2)
  {
    Console.Write("Function doesn't support " +
                  "numbers of different " +
                  "lengths. If you want to " +
                  "dd such numbers then " +
                  "prefix smaller number " +
                  "with required no. of zeroes");
  }

  // Note the size of the allocated
  // memory is one more than i/p
  // lengths for the cases where we
  // have carry at the last like
  // adding D1 and A1
  res = new char[(4 * (l1 + 1))];

  // Add all numerals from
  // right to left
  for(i = l1 - 1; i >= 0; i--)
  {
    // Get decimal values of the
    // numerals of i/p numbers
    nml1 = getNumeralValue(num1[i]);
    nml2 = getNumeralValue(num2[i]);

    // Add decimal values of
    // numerals and carry
    res_nml = carry + nml1 + nml2;

    // Check if we have carry for
    // next addition of numerals
    if(res_nml >= 14)
    {
      carry = 1;
      res_nml -= 14;
    }
    else
    {
      carry = 0;
    }
    res[i + 1] = getNumeral(res_nml);
  }

  // If there is no carry after
  // last iteration then result
  // should not include 0th
  // character of the resultant
  // String
  if(carry == 0)
    return String.Join("", res);

  // If we have carry after last
  // iteration then result should
  // include 0th character
  res[0] = '1';
  return String.Join("", res);
}

// Function to get value of a numeral
// For example it returns 10 for input
// 'A' 1 for '1', etc
static int getNumeralValue(char num)
{
  if(num >= '0' && num <= '9')
    return (num - '0');
  if(num >= 'A' && num <= 'D')
    return (num - 'A' + 10);

  // If we reach this line
  // caller is giving invalid
  // character so we assert
  // and fail
  // assert(0);
  return 0;
}

// Function to get numeral
// for a value. For example
// it returns 'A' for input 10
// '1' for 1, etc
static char getNumeral(int val)
{
  if(val >= 0 && val <= 9)
    return (char)(val + '0');
  if(val >= 10 && val <= 14)
    return (char)(val + 'A' - 10);

  // If we reach this line
  // caller is giving invalid
  // no. so we assert and fail
  // assert(0);
  return '0';
}

// Driver code
public static void Main(String[] args)
{
  char []num1 = {'D','C','2'};
  char []num2 = {'0','A','3'};
  Console.Write("Result is " +
                sumBase14(num1,
                          num2));
}
}

// This code is contributed by Rajput-Ji

Javascript

<script>
    // Function to add two
    // numbers in base 14
    function sumBase14(num1,num2)
    {
        let l1 = num1.length;
        let l2 = num2.length;

        // Note the size of the allocated
        // memory is one more than i/p
        // lengths for the cases where we
        // have carry at the last like
        // adding D1 and A1
        let res = new Array(4 * (l1 + 1));
        let i = 0;
        let nml1 = 0, nml2 = 0, res_nml = 0;
        let carry = 0;
        if(l1 != l2)
        {
            document.write("Function doesn't support " +
                     "numbers of different " +
                     "lengths. If you want to " +
                     "dd such numbers then " +
                     "prefix smaller number " +
                     "with required no. of zeroes");

        }

        // Add all numerals from
        // right to left
        for(i = l1 - 1; i >= 0; i--)
        {

            // Get decimal values of the
            // numerals of i/p numbers
            nml1 = getNumeralValue(num1[i]);
            nml2 = getNumeralValue(num2[i]);

            // Add decimal values of
            // numerals and carry
            res_nml = carry + nml1 + nml2;

            // Check if we have carry for
            // next addition of numerals
            if(res_nml >= 14)
            {
                carry = 1;
                res_nml -= 14;
            }
            else
            {
                carry = 0;
            }
            res[i + 1] = getNumeral(res_nml);
        }

        // If there is no carry after
        // last iteration then result
        // should not include 0th
        // character of the resultant
        // String
        if(carry == 0)
        {
            return res;
        }

        // If we have carry after last
        // iteration then result should
        // include 0th character
        res[0] = '1';
        return res.join('');
    }

    // Function to get value of a numeral
    // For example it returns 10 for input
    // 'A' 1 for '1', etc
    function getNumeralValue(num)
    {
        if(num >= '0' && num <= '9')
        {
            return (num.charCodeAt(0) - '0'.charCodeAt(0));
        }
        if(num >= 'A' && num <= 'D')
        {
            return (num.charCodeAt(0) - 'A'.charCodeAt(0) + 10);
        }

        // If we reach this line
        // caller is giving invalid
        // character so we assert
        // and fail
        // assert(0);
        return 0;
    }

    // Function to get numeral
    // for a value. For example
    // it returns 'A' for input 10
    // '1' for 1, etc
    function getNumeral(val)
    {
        if(val >= 0 && val <= 9)
        {
            return String.fromCharCode(val + '0'.charCodeAt(0));
        }
        if(val >= 10 && val <= 14)
        {
            return String.fromCharCode(val + 'A'.charCodeAt(0) - 10);
        }

        // If we reach this line
        // caller is giving invalid
        // no. so we assert and fail
        // assert(0);
        return 0;
    }

    // Driver code
    let num1 = ['D','C','2'];
    let num2 = ['0','A','3'];

    document.write("Result is " + sumBase14(num1, num2));

    // This code is contributed by avanitrachhadiya2155
</script>

Output:

Result is 1085

Time Complexity: O(|num1|)

Auxiliary Space: O(|num1|)

Notes:
The above approach can be used to add numbers to any base. We don’t have to do string operations if the base is smaller than 10.
You can try extending the above program for numbers of different lengths. 
Please comment if you find any bug in the program or a better approach to do the same.