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Convert a number from base A to base B

  • Difficulty Level : Medium
  • Last Updated : 10 Nov, 2021

Given two positive integers A and B and a string S of size N,  denoting a number in base A, the task is to convert the given string S from base A to base B.

Examples:

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Input: S = “10B”, A = 16, B = 10
Output: 267
Explanation: 10B in hexadecimal (base =16) when converted to decimal (base =10) is 267.

Input: S = “10011”, A = 2, B = 8
Output: 23
Explanation: 10011 in binary (base =2) when converted to octal (base = 8) is 23. 



Approach: Number systemsis the technique to represent numbers in the computer system architecture. The computer architecture supports the following number systems:

  • Binary Number System (Base 2): The binary number system only consists of two digits, 0s and 1s. The base of this number system is 2.
  • Octal Number System (Base 8): The octal number system consists of 8 digits ranging from 0 to 7.
  • Decimal Number System (Base 10): The decimal number system consists of 10 digits ranging from 0 to 9.
  • Hexadecimal Number System (Base 16): The hexadecimal number system consists of 16 digits with 0 to 9 digits and alphabets A to F. It is also known as alphanumeric code as it consists of both number and alphabets.

To convert a number from base A to base B, the idea is to first convert it to its decimal representation and then convert the decimal number to base B 

Conversion from any base to Decimal: The decimal equivalent of the number “str” in base “base” is equal to 1 * str[len – 1] + base * str[len – 2] + (base)2 * str[len – 3] + …

Conversion from Decimal to any base: 
The decimal number “inputNum” can be converted to a number on base “base” by repeatedly dividing inputNum by base and store the remainder. Finally, reverse the obtained string to get the desired result. 

Below is the implementation of the above approach:

C++




// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to return ASCII
// value of a character
int val(char c)
{
    if (c >= '0' && c <= '9')
        return (int)c - '0';
    else
        return (int)c - 'A' + 10;
}
 
// Function to convert a number
// from given base to decimal number
int toDeci(string str, int base)
{
    // Stores the length
    // of the string
    int len = str.size();
 
    // Initialize power of base
    int power = 1;
 
    // Initialize result
    int num = 0;
 
    // Decimal equivalent is str[len-1]*1
    // + str[len-2]*base + str[len-3]*(base^2) + ...
    for (int i = len - 1; i >= 0; i--) {
 
        // A digit in input number must
        // be less than number's base
        if (val(str[i]) >= base) {
            printf("Invalid Number");
            return -1;
        }
 
        // Update num
        num += val(str[i]) * power;
 
        // Update power
        power = power * base;
    }
 
    return num;
}
 
// Function to return equivalent
// character of a given value
char reVal(int num)
{
    if (num >= 0 && num <= 9)
        return (char)(num + '0');
    else
        return (char)(num - 10 + 'A');
}
 
// Function to convert a given
// decimal number to a given base
string fromDeci(int base, int inputNum)
{
    // Store the result
    string res = "";
 
    // Repeatedly divide inputNum
    // by base and take remainder
    while (inputNum > 0) {
 
        // Update res
        res += reVal(inputNum % base);
 
        // Update inputNum
        inputNum /= base;
    }
 
    // Reverse the result
    reverse(res.begin(), res.end());
 
    return res;
}
 
// Function to convert a given number
// from a base to another base
void convertBase(string s, int a, int b)
{
    // Convert the number from
    // base A to decimal
    int num = toDeci(s, a);
 
    // Convert the number from
    // decimal to base B
    string ans = fromDeci(b, num);
 
    // Print the result
    cout << ans;
}
 
// Driver Code
int main()
{
    // Given input
    string s = "10B";
    int a = 16, b = 10;
 
    // Function Call
    convertBase(s, a, b);
 
    return 0;
}

Java




// Java program for the above approach
import java.util.*;
 
class GFG{
 
// Function to return ASCII
// value of a character
static int val(char c)
{
    if (c >= '0' && c <= '9')
        return(int)c - '0';
    else
        return(int)c - 'A' + 10;
}
 
// Function to convert a number
// from given base to decimal number
static int toDeci(String str, int base)
{
     
    // Stores the length
    // of the String
    int len = str.length();
 
    // Initialize power of base
    int power = 1;
 
    // Initialize result
    int num = 0;
 
    // Decimal equivalent is str[len-1]*1
    // + str[len-2]*base + str[len-3]*(base^2) + ...
    for(int i = len - 1; i >= 0; i--)
    {
         
        // A digit in input number must
        // be less than number's base
        if (val(str.charAt(i)) >= base)
        {
            System.out.printf("Invalid Number");
            return -1;
        }
 
        // Update num
        num += val(str.charAt(i)) * power;
 
        // Update power
        power = power * base;
    }
    return num;
}
 
// Function to return equivalent
// character of a given value
static char reVal(int num)
{
    if (num >= 0 && num <= 9)
        return(char)(num + '0');
    else
        return(char)(num - 10 + 'A');
}
 
// Function to convert a given
// decimal number to a given base
static String fromDeci(int base, int inputNum)
{
     
    // Store the result
    String res = "";
 
    // Repeatedly divide inputNum
    // by base and take remainder
    while (inputNum > 0)
    {
         
        // Update res
        res += reVal(inputNum % base);
 
        // Update inputNum
        inputNum /= base;
    }
 
    // Reverse the result
    res = reverse(res);
 
    return res;
}
 
// Function to convert a given number
// from a base to another base
static void convertBase(String s, int a, int b)
{
     
    // Convert the number from
    // base A to decimal
    int num = toDeci(s, a);
 
    // Convert the number from
    // decimal to base B
    String ans = fromDeci(b, num);
 
    // Print the result
    System.out.print(ans);
}
 
static String reverse(String input)
{
    char[] a = input.toCharArray();
    int l, r = a.length - 1;
    for(l = 0; l < r; l++, r--)
    {
        char temp = a[l];
        a[l] = a[r];
        a[r] = temp;
    }
    return String.valueOf(a);
}
 
// Driver Code
public static void main(String[] args)
{
     
    // Given input
    String s = "10B";
    int a = 16, b = 10;
 
    // Function Call
    convertBase(s, a, b);
}
}
 
// This code is contributed by 29AjayKumar

Python3




# Python program for the above approach
 
# Function to return ASCII
# value of a character
def val(c):
    if (c >= '0' and c <= '9'):
        return ord(c) - 48
    else:
        return ord(c) - 65  + 10
 
# Function to convert a number
# from given base to decimal number
def toDeci(strr, base):
     
    # Stores the length
    # of the string
    lenn = len(strr)
     
    # Initialize power of base
    power = 1
     
    # Initialize result
    num = 0
     
    # Decimal equivalent is strr[len-1]*1
    # + strr[len-2]*base + strr[len-3]*(base^2) + ...
    for i in range(lenn - 1, -1, -1):
        # A digit in input number must
        # be less than number's base
        if (val(strr[i]) >= base):
            print("Invalid Number")
            return -1
             
        # Update num
        num += val(strr[i]) * power
         
        # Update power
        power = power * base
     
    return num
 
# Function to return equivalent
# character of a given value
def reVal(num):
     
    if (num >= 0 and num <= 9):
        return chr(num + 48)
    else:
        return chr(num - 10 + 65)
 
 
# Function to convert a given
# decimal number to a given base
def fromDeci(base, inputNum):
     
    # Store the result
    res = ""
     
    # Repeatedly divide inputNum
    # by base and take remainder
    while (inputNum > 0):
         
        # Update res
        res += reVal(inputNum % base)
         
        # Update inputNum
        inputNum //= base
         
    # Reverse the result
    res = res[::-1]
     
    return res
 
 
# Function to convert a given number
# from a base to another base
def convertBase(s, a, b):
     
    # Convert the number from
    # base A to decimal
    num = toDeci(s, a)
 
    # Convert the number from
    # decimal to base B
    ans = fromDeci(b, num)
 
    # Print the result
    print(ans)
 
 
# Driver Code
 
# Given input
s = "10B"
a = 16
b = 10
 
# Function Call
convertBase(s, a, b)
 
# This code is contributed by shubhamsingh10

C#




// C# program for the above approach
using System;
 
public class GFG{
     
    // Function to return ASCII
    // value of a character
    static int val(char c)
    {
        if (c >= '0' && c <= '9')
            return(int)c - '0';
        else
            return(int)c - 'A' + 10;
    }
     
    // Function to convert a number
    // from given basse to decimal number
    static int toDeci(string str, int basse)
    {
         
        // Stores the length
        // of the string
        int len = str.Length;
     
        // Initialize power of basse
        int power = 1;
     
        // Initialize result
        int num = 0;
     
        // Decimal equivalent is str[len-1]*1
        // + str[len-2]*basse + str[len-3]*(basse^2) + ...
        for(int i = len - 1; i >= 0; i--)
        {
             
            // A digit in input number must
            // be less than number's basse
            if (val(str[i]) >= basse)
            {
                Console.Write("Invalid Number");
                return -1;
            }
     
            // Update num
            num += val(str[i]) * power;
     
            // Update power
            power = power * basse;
        }
        return num;
    }
     
    // Function to return equivalent
    // character of a given value
    static char reVal(int num)
    {
        if (num >= 0 && num <= 9)
            return(char)(num + '0');
        else
            return(char)(num - 10 + 'A');
    }
     
    // Function to convert a given
    // decimal number to a given basse
    static string fromDeci(int basse, int inputNum)
    {
         
        // Store the result
        string res = "";
     
        // Repeatedly divide inputNum
        // by basse and take remainder
        while (inputNum > 0)
        {
             
            // Update res
            res += reVal(inputNum % basse);
     
            // Update inputNum
            inputNum /= basse;
        }
     
        // Reverse the result
        res = reverse(res);
     
        return res;
    }
     
    // Function to convert a given number
    // from a basse to another basse
    static void convertbasse(string s, int a, int b)
    {
         
        // Convert the number from
        // basse A to decimal
        int num = toDeci(s, a);
     
        // Convert the number from
        // decimal to basse B
        string ans = fromDeci(b, num);
     
        // Print the result
        Console.Write(ans);
    }
     
    static string reverse(string input)
    {
        char[] a = input.ToCharArray();
        int l, r = a.Length - 1;
        for(l = 0; l < r; l++, r--)
        {
            char temp = a[l];
            a[l] = a[r];
            a[r] = temp;
        }
        return new string(a);
    }
     
    // Driver Code
    static public void Main (){
        // Given input
        string s = "10B";
        int a = 16, b = 10;
     
        // Function Call
        convertbasse(s, a, b);
    }
}
 
// This code is contributed by shubhamsingh10

Javascript




<script>
// Javascript program for the above approach
 
// Function to return ASCII
// value of a character
function val(c)
{
    if (c >= '0' && c <= '9')
        return c.charCodeAt(0) - 48;
    else
        return c.charCodeAt(0) - 65 + 10;
}
 
// Function to convert a number
// from given base to decimal number
function toDeci(str, base)
{
 
    // Stores the length
    // of the var
    var len = str.length;
 
    // Initialize power of base
    var power = 1;
 
    // Initialize result
    var num = 0;
 
    // Decimal equivalent is str[len-1]*1
    // + str[len-2]*base + str[len-3]*(base^2) + ...
    for (var i = len - 1; i >= 0; i--) {
 
        // A digit in input number must
        // be less than number's base
        if (val(str[i]) >= base) {
            document.write("Invalid Number");
            return -1;
        }
         
        // Update num
        num += val(str[i]) * power;
         
 
        // Update power
        power = power * base;
    }
 
    return num;
}
 
// Function to return equivalent
// character of a given valueString.fromCharCode
function reVal(num)
{
    if (num >= 0 && num <= 9)
        return String.fromCharCode(num + 48);
    else
        return String.fromCharCode(num - 10 + 65);
}
 
// Function to convert a given
// decimal number to a given base
function fromDeci(base, inputNum)
{
 
    // Store the result
    var res = "";
 
    // Repeatedly divide inputNum
    // by base and take remainder
    while (inputNum > 0) {
 
        // Update res
        res += reVal(inputNum % base);
 
        // Update inputNum
        inputNum = Math.floor(inputNum/base);
    }
 
    // Reverse the result
    res = res.split("").reverse().join("");
 
    return res;
}
 
// Function to convert a given number
// from a base to another base
function convertBase(s, a, b)
{
 
    // Convert the number from
    // base A to decimal
    var num = toDeci(s, a);
 
    // Convert the number from
    // decimal to base B
    var ans = fromDeci(b, num);
 
    // Prvar the result
    document.write(ans);
}
 
// Driver Code
// Given input
var s = "10B";
var a = 16
var b = 10;
 
// Function Call
convertBase(s, a, b);
 
// This code is contributed by ShubhamSingh10
</script>
Output: 
267

 

Time Complexity: O(N)
Auxiliary Space: O(N)

 




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