Complement of a number with any base b

In this post, a general method of finding complement with any arbitrary base is discussed.

Remember: It is recommended to go through below as follows:

• One’s Complement of an Integer
• 1’s and 2’s complement of a Binary Number

Steps to find (b-1)’s complement: To find (b-1)’s complement, 

• Subtract each digit of the number from the largest number in the number system with base .
• For example, if the number is a three-digit number in base 9, then subtract the number from 888 as 8 is the largest number in base 9 number system.
• The obtained result is the (b-1)’s (8’s complement) complement.

Steps to find b’s complement: To find b’s complement, just add 1 to the calculated (b-1)’s complement. Now, this holds true for any base in the number system that exists. It can be tested with familiar bases that is the 1’s and 2’s complement.

Example: 

Let the number be 10111 base 2 (b=2)
Then, 1's complement will be 01000 (b-1)
2's complement will be 01001 (b)

Taking a number with Octal base:
Let the number be -456.
Then 7's complement will be 321
and 8's complement will be 322

Below is the implementation of the above idea as follows:  

C++

// CPP program to find complement of a
// number with any base b

#include <cmath>
#include <iostream>

using namespace std;

// Function to find (b-1)'s complement
int prevComplement(int n, int b)
{
    int maxDigit, maxNum = 0, digits = 0, num = n;

    // Calculate number of digits
    // in the given number
    while (n != 0) {
        digits++;
        n = n / 10;
    }

    // Largest digit in the number
    // system with base b
    maxDigit = b - 1;

    // Largest number in the number
    // system with base b
    while (digits--) {
        maxNum = maxNum * 10 + maxDigit;
    }

    // return Complement
    return maxNum - num;
}

// Function to find b's complement
int complement(int n, int b)
{
    // b's complement = (b-1)'s complement + 1
    return prevComplement(n, b) + 1;
}

// Driver code
int main()
{
    cout << prevComplement(25, 7) << endl;

    cout << complement(25, 7);

    return 0;
}

Java

// Java program to find complement
// of a number with any base b
class GFG
{

// Function to find (b-1)'s complement
static int prevComplement(int n, int b)
{
    int maxDigit, maxNum = 0,
        digits = 0, num = n;

    // Calculate number of digits
    // in the given number
    while(n != 0)
    {
        digits++;
        n = n / 10;
    }

    // Largest digit in the number
    // system with base b
    maxDigit = b - 1;

    // Largest number in the number
    // system with base b
    while((digits--) > 0)
    {
        maxNum = maxNum * 10 + maxDigit;
    }

    // return Complement
    return maxNum - num;
}

// Function to find b's complement
static int complement(int n, int b)
{
    // b's complement = (b-1)'s
    // complement + 1
    return prevComplement(n, b) + 1;
}

// Driver code
public static void main(String args[])
{
    System.out.println(prevComplement(25, 7));

    System.out.println(complement(25, 7));
}
}

// This code is contributed
// by Kirti_Mangal

Python 3

# Python 3 program to find
# complement of a number
# with any base b

# Function to find
# (b-1)'s complement
def prevComplement(n, b) :
    maxNum, digits, num = 0, 0, n

    # Calculate number of digits
    # in the given number
    while n > 1 :
        digits += 1
        n = n // 10

    # Largest digit in the number
    # system with base b
    maxDigit = b - 1

    # Largest number in the number
    # system with base b
    while digits :
        maxNum = maxNum * 10 + maxDigit
        digits -= 1

    # return Complement
    return maxNum - num

# Function to find b's complement
def complement(n, b) :

    # b's complement = (b-1)'s
    # complement + 1
    return prevComplement(n, b) + 1

# Driver code
if __name__ == "__main__" :

    # Function calling
    print(prevComplement(25, 7))
    print(complement(25, 7))

# This code is contributed
# by ANKITRAI1

C#

// C# program to find complement
// of a number with any base b
class GFG
{

// Function to find (b-1)'s complement
static int prevComplement(int n, int b)
{
    int maxDigit, maxNum = 0,
        digits = 0, num = n;

    // Calculate number of digits
    // in the given number
    while(n != 0)
    {
        digits++;
        n = n / 10;
    }

    // Largest digit in the number
    // system with base b
    maxDigit = b - 1;

    // Largest number in the number
    // system with base b
    while((digits--) > 0)
    {
        maxNum = maxNum * 10 + maxDigit;
    }

    // return Complement
    return maxNum - num;
}

// Function to find b's complement
static int complement(int n, int b)
{
    // b's complement = (b-1)'s
    // complement + 1
    return prevComplement(n, b) + 1;
}

// Driver code
public static void Main()
{
    System.Console.WriteLine(prevComplement(25, 7));

    System.Console.WriteLine(complement(25, 7));
}
}

// This code is contributed
// by mits

PHP

<?php
// PHP program to find complement
// of a number with any base b

// Function to find (b-1)'s complement
function prevComplement($n, $b)
{
    $maxNum = 0;
    $digits = 0;
    $num = $n;

    // Calculate number of digits
    // in the given number
    while((int)$n != 0)
    {
        $digits++;
        $n = $n / 10;
    }

    // Largest digit in the number
    // system with base b
    $maxDigit = $b - 1;

    // Largest number in the number
    // system with base b
    while($digits--)
    {
        $maxNum = $maxNum * 10 +
                  $maxDigit;
    }

    // return Complement
    return $maxNum - $num;
}

// Function to find b's complement
function complement($n, $b)
{
    // b's complement = (b-1)'s
    // complement + 1
    return prevComplement($n, $b) + 1;
}

// Driver code
echo prevComplement(25, 7), "\n";

echo(complement(25, 7));

// This code is contributed
// by Smitha
?>

Javascript

<script>

// Javascript program to find complement
// of a number with any base b

// Function to find (b-1)'s complement
    function prevComplement(n , b) {
        var maxDigit, maxNum = 0, digits = 0,
        num = n;

        // Calculate number of digits
        // in the given number
        while (n != 0) {
            digits++;
            n = parseInt(n / 10);
        }

        // Largest digit in the number
        // system with base b
        maxDigit = b - 1;

        // Largest number in the number
        // system with base b
        while ((digits--) > 0) {
            maxNum = maxNum * 10 + maxDigit;
        }

        // return Complement
        return maxNum - num;
    }

    // Function to find b's complement
    function complement(n , b) {
        // b's complement = (b-1)'s
        // complement + 1
        return prevComplement(n, b) + 1;
    }

    // Driver code

        document.write(prevComplement(25, 7)+"<br/>");

        document.write(complement(25, 7));

// This code is contributed by todaysgaurav

</script>

Output:

41
42

Time Complexity: O(log n)

Auxiliary Space: O(1)