Convert from any base to decimal and vice versa

Last Updated : 26 Dec, 2023

Given a number and its base, convert it to decimal. The base of number can be anything such that all digits can be represented using 0 to 9 and A to Z. The value of A is 10, the value of B is 11 and so on. Write a function to convert the number to decimal.

Examples: 

Input number is given as string and output is an integer.
Input: str = "1100", base = 2 
Output: 12
Input: str = "11A", base = 16
Output: 282
Input: str = "123",  base = 8
Output: 83


We strongly recommend you to minimize your browser and try this yourself first. 
We can always use the below formula to convert from any base to decimal.

"str" is input number as a string 
"base" is the base of the input number.
Decimal Equivalent is,
  1*str[len-1] + base*str[len-2] + (base)2*str[len-3] + ...

Below is implementation of above formula.  

Try It Yourself
redirect icon
C++ 
// C++ program of the above approach
#include <bits/stdc++.h>
using namespace std;

// To return char for a value. For example '2'
// is returned for 2. 'A' is returned for 10. 'B'
// for 11
char reVal(int num)
{
    if (num >= 0 && num <= 9)
        return (char)(num + '0');
    else
        return (char)(num - 10 + 'A');
}

// Utility function to reverse a string
void strev(char *str)
{
    int len = strlen(str);
    int i;
    for (i = 0; i < len/2; i++)
    {
        char temp = str[i];
        str[i] = str[len-i-1];
        str[len-i-1] = temp;
    }
}

// Function to convert a given decimal number
// to a base 'base' and
char* fromDeci(char res[], int base, int inputNum)
{
    int index = 0; // Initialize index of result

    // Convert input number is given base by repeatedly
    // dividing it by base and taking remainder
    while (inputNum > 0)
    {
        res[index++] = reVal(inputNum % base);
        inputNum /= base;
    }
    res[index] = '\0';

    // Reverse the result
    strev(res);

    return res;
}

// Driver Code
int main()
{
    int inputNum = 282, base = 16;
    char res[100];
    cout << "Decimal Equivalent of " << fromDeci(res, base, inputNum) << " in base "<< base << " is " << 
                                            inputNum;

    return 0;
}

// This code is contributed by code_hunt.
C 
// C program to convert a number from any base
// to decimal
#include <stdio.h>
#include <string.h>

// To return value of a char. For example, 2 is
// returned for '2'.  10 is returned for 'A', 11
// for 'B'
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 'b'
// to decimal
int toDeci(char *str, int base)
{
    int len = strlen(str);
    int power = 1; // Initialize power of base
    int num = 0;  // Initialize result
    int i;

    // Decimal equivalent is str[len-1]*1 +
    // str[len-2]*base + str[len-3]*(base^2) + ...
    for (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;
        }

        num += val(str[i]) * power;
        power = power * base;
    }

    return num;
}

// Driver code
int main()
{
    char str[] = "11A";
    int base = 16;
    printf("Decimal equivalent of %s in base %d is "
           " %d\n", str, base, toDeci(str, base));
    return 0;
}
Java 
// Java program to convert 
// a number from any base
// to decimal
import java.io.*;

class GFG 
{
// To return value of a char. 
// For example, 2 is returned
// for '2'. 10 is returned 
// for 'A', 11 for 'B'
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 
// 'b' to decimal
static int toDeci(String str, 
                  int base)
{
    int len = str.length();
    int power = 1; // Initialize 
                   // power of base
    int num = 0; // Initialize result
    int i;

    // Decimal equivalent is 
    // str[len-1]*1 + str[len-2] *
    // base + str[len-3]*(base^2) + ...
    for (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.println("Invalid Number");
        return -1;
        }

        num += val(str.charAt(i)) * power;
        power = power * base;
    }

    return num;
}

// Driver code
public static void main (String[] args) 
{
    String str = "11A";
    int base = 16;
    System.out.println("Decimal equivalent of "+ 
                        str + " in base "+ base + 
                                     " is "+ " "+ 
                              toDeci(str, base));
}
}

// This code is contributed 
// by anuj_67.
Python3 
# Python program to convert a 
# number from any base to decimal

# To return value of a char. 
# For example, 2 is returned 
# for '2'. 10 is returned for 'A', 
# 11 for 'B' 
def val(c):
    if c >= '0' and c <= '9':
        return ord(c) - ord('0')
    else:
        return ord(c) - ord('A') + 10;

# Function to convert a number 
# from given base 'b' to decimal 
def toDeci(str,base):
    llen = len(str)
    power = 1 #Initialize power of base
    num = 0     #Initialize result

    # Decimal equivalent is str[len-1]*1 + 
    # str[len-2]*base + str[len-3]*(base^2) + ... 
    for i in range(llen - 1, -1, -1):
        
        # A digit in input number must 
        # be less than number's base 
        if val(str[i]) >= base:
            print('Invalid Number')
            return -1
        num += val(str[i]) * power
        power = power * base
    return num
    
# Driver code
strr = "11A"
base = 16
print('Decimal equivalent of', strr, 
              'in base', base, 'is', 
                 toDeci(strr, base))

# This code is contributed 
# by Sahil shelangia
C# 
// C# program to convert 
// a number from any base
// to decimal
using System;

class GFG 
{
// To return value of a char. 
// For example, 2 is returned
// for '2'. 10 is returned 
// for 'A', 11 for 'B'
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 
// 'b' to decimal
static int toDeci(string str, 
                  int b_ase)
{
    int len = str.Length;
    int power = 1; // Initialize 
                   // power of base
    int num = 0; // Initialize result
    int i;

    // Decimal equivalent is 
    // str[len-1]*1 + str[len-2] *
    // base + str[len-3]*(base^2) + ...
    for (i = len - 1; i >= 0; i--)
    {
        // A digit in input number 
        // must be less than 
        // number's base
        if (val(str[i]) >= b_ase)
        {
        Console.WriteLine("Invalid Number");
        return -1;
        }

        num += val(str[i]) * power;
        power = power * b_ase;
    }

    return num;
}

// Driver code
public static void Main () 
{
    string str = "11A";
    int b_ase = 16;
    Console.WriteLine("Decimal equivalent of "+ 
                     str + " in base "+ b_ase + 
                  " is " + toDeci(str, b_ase));
}
}

// This code is contributed 
// by anuj_67.
JavaScript 
<script>

// Javascript program to convert 
// a number from any base
// to decimal

// To return value of a char. 
// For example, 2 is returned
// for '2'. 10 is returned 
// for 'A', 11 for 'B'
function val(c)
{
    if (c >= '0'.charCodeAt() && 
        c <= '9'.charCodeAt())
        return (c - '0'.charCodeAt());
    else
        return (c - 'A'.charCodeAt() + 10);
}

// Function to convert a 
// number from given base 
// 'b' to decimal
function toDeci(str, b_ase)
{
    let len = str.length;
    
    // Initialize 
    // power of base
    let power = 1; 
    
    // Initialize result
    let num = 0; 
    let i;

    // Decimal equivalent is 
    // str[len-1]*1 + str[len-2] *
    // base + str[len-3]*(base^2) + ...
    for(i = len - 1; i >= 0; i--)
    {
        
        // A digit in input number 
        // must be less than 
        // number's base
        if (val(str[i].charCodeAt()) >= b_ase)
        {
            document.write("Invalid Number");
            return -1;
        }

        num += val(str[i].charCodeAt()) * power;
        power = power * b_ase;
    }
    return num;
}

// Driver code 
let str = "11A";
let b_ase = 16;

document.write("Decimal equivalent of "+ 
               str + " in base "+ b_ase + 
               " is " + toDeci(str, b_ase));
               
// This code is contributed by divyesh072019

</script>
PHP 
<?php
// PHP program to convert a number from 
// any base to decimal

// To return value of a char. For example,
// 2 is returned for '2'. 10 is returned
// for 'A', 11 for 'B'
function val($c)
{
    if ($c >= '0' && $c <= '9')
        return ord($c) - ord('0');
    else
        return ord($c) - ord('A') + 10;
}

// Function to convert a number from given 
// base 'b' to decimal
function toDeci($str, $base)
{
    $len = strlen($str);
    $power = 1; // Initialize power of base
    $num = 0; // Initialize result

    // Decimal equivalent is str[len-1]*1 +
    // str[len-2]*base + str[len-3]*(base^2) + ...
    for ($i = $len - 1; $i >= 0; $i--)
    {
        // A digit in input number must be
        // less than number's base
        if (val($str[$i]) >= $base)
        {
            print("Invalid Number");
            return -1;
        }

        $num += val($str[$i]) * $power;
        $power = $power * $base;
    }

    return $num;
}

// Driver code
$str = "11A";
$base = 16;
print("Decimal equivalent of $str " . 
      "in base $base is " . toDeci($str, $base));

// This code is contributed by mits
?>

Output
Decimal equivalent of 11A in base 16 is  282

Time Complexity: O(N) n represents the length of string
Auxiliary Space: O(1)

How to do reverse? 

Let the given input decimal number be "inputNum" and target base be "base". We repeatedly divide inputNum by base and store the remainder. We finally reverse the obtained string. Below is C implementation.

C++ 
// C++ Program to convert decimal to any given base
#include <bits/stdc++.h>
using namespace std;

// To return char for a value. For example '2'
// is returned for 2. 'A' is returned for 10. 'B'
// for 11
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 base 'base' and
string fromDeci(string& res, int base, int inputNum)
{
    int index = 0; // Initialize index of result

    // Convert input number is given base by repeatedly
    // dividing it by base and taking remainder
    while (inputNum > 0) {
        res.push_back(reVal(inputNum % base));
        index++;
        inputNum /= base;
    }

    // Reverse the result
    reverse(res.begin(), res.end());

    return res;
}

// Driver program
int main()
{
    int inputNum = 282, base = 16;
    string res;
    cout << "Equivalent of " << inputNum << " in base "
         << base << " is " << fromDeci(res, base, inputNum)
         << endl;

    return 0;
}

// The code is contributed by Gautam goel (gautamgoel962)
C 
// C Program to convert decimal to any given base
#include <stdio.h>
#include <string.h>

// To return char for a value. For example '2'
// is returned for 2. 'A' is returned for 10. 'B'
// for 11
char reVal(int num)
{
    if (num >= 0 && num <= 9)
        return (char)(num + '0');
    else
        return (char)(num - 10 + 'A');
}

// Utility function to reverse a string
void strev(char *str)
{
    int len = strlen(str);
    int i;
    for (i = 0; i < len/2; i++)
    {
        char temp = str[i];
        str[i] = str[len-i-1];
        str[len-i-1] = temp;
    }
}

// Function to convert a given decimal number
// to a base 'base' and
char* fromDeci(char res[], int base, int inputNum)
{
    int index = 0;  // Initialize index of result

    // Convert input number is given base by repeatedly
    // dividing it by base and taking remainder
    while (inputNum > 0)
    {
        res[index++] = reVal(inputNum % base);
        inputNum /= base;
    }
    res[index] = '\0';

    // Reverse the result
    strev(res);

    return res;
}

// Driver program
int main()
{
    int inputNum = 282, base = 16;
    char res[100];
    printf("Equivalent of %d in base %d is "
           " %s\n", inputNum, base, fromDeci(res, base, inputNum));
    return 0;
}
Java 
// Java Program to convert decimal to any given base
import java.lang.*; 
import java.io.*; 
import java.util.*; 

class GFG
{
    
// To return char for a value. For 
// example '2' is returned for 2. 
// 'A' is returned for 10. 'B' for 11
static char reVal(int num)
{
    if (num >= 0 && num <= 9)
        return (char)(num + 48);
    else
        return (char)(num - 10 + 65);
}

// Function to convert a given decimal number
// to a base 'base' and
static String fromDeci(int base1, int inputNum)
{
    String s = "";

    // Convert input number is given 
    // base by repeatedly dividing it
    // by base and taking remainder
    while (inputNum > 0)
    {
        s += reVal(inputNum % base1);
        inputNum /= base1;
    }
    StringBuilder ix = new StringBuilder(); 

        // append a string into StringBuilder input1 
        ix.append(s); 

    // Reverse the result
    return new String(ix.reverse());
}

// Driver code
public static void main (String[] args)
{
    int inputNum = 282, base1 = 16;
    System.out.println("Equivalent of " + inputNum +
                            " in base "+base1+" is " +
                            fromDeci(base1, inputNum));
}
}

// This code is contributed by mits
Python3 
# Python3 Program to convert decimal to 
# any given base

# To return char for a value. For example 
# '2' is returned for 2. 'A' is returned 
# for 10. 'B' for 11
def reVal(num):

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

# Utility function to reverse a string
def strev(str):

    len = len(str);
    for i in range(int(len / 2)):
        temp = str[i];
        str[i] = str[len - i - 1];
        str[len - i - 1] = temp;

# Function to convert a given decimal 
# number to a base 'base' and
def fromDeci(res, base, inputNum):

    index = 0; # Initialize index of result

    # Convert input number is given base 
    # by repeatedly dividing it by base 
    # and taking remainder
    while (inputNum > 0):
        res+= reVal(inputNum % base);
        inputNum = int(inputNum / base);

    # Reverse the result
    res = res[::-1];

    return res;

# Driver Code
inputNum = 282;
base = 16;
res = "";
print("Equivalent of", inputNum, "in base", 
       base, "is", fromDeci(res, base, inputNum));

# This code is contributed by mits
C# 
// C# Program to convert decimal to any given base
using System;
using System.Collections;

class GFG
{
    
// To return char for a value. For 
// example '2' is returned for 2. 
// 'A' is returned for 10. 'B' for 11
static char reVal(int num)
{
    if (num >= 0 && num <= 9)
        return (char)(num + 48);
    else
        return (char)(num - 10 + 65);
}

// Function to convert a given decimal number
// to a base 'base' and
static string fromDeci(int base1, int inputNum)
{
    string s = "";

    // Convert input number is given 
    // base by repeatedly dividing it
    // by base and taking remainder
    while (inputNum > 0)
    {
        s += reVal(inputNum % base1);
        inputNum /= base1;
    }
    char[] res = s.ToCharArray();

    // Reverse the result
    Array.Reverse(res);
    return new String(res);
}

// Driver code
static void Main()
{
    int inputNum = 282, base1 = 16;
    Console.WriteLine("Equivalent of " + inputNum +
                            " in base "+base1+" is " +
                            fromDeci(base1, inputNum));
}
}

// This code is contributed by mits
JavaScript 
<script>
    // Javascript Program to convert decimal to any given base
    
    // To return char for a value. For
    // example '2' is returned for 2.
    // 'A' is returned for 10. 'B' for 11
    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 base 'base' and
    function fromDeci(base1, inputNum)
    {
        let s = "";

        // Convert input number is given
        // base by repeatedly dividing it
        // by base and taking remainder
        while (inputNum > 0)
        {
            s += reVal(inputNum % base1);
            inputNum = parseInt(inputNum / base1, 10);
        }
        let res = s.split('');

        // Reverse the result
        res.reverse();
        return res.join("");
    }
    
    let inputNum = 282, base1 = 16;
    document.write("Equivalent of " + inputNum +
                            " in base "+base1+" is " +
                            fromDeci(base1, inputNum));

// This code is contributed by rameshtravel07.
</script>
PHP 
<?php
// PHP Program to convert decimal to 
// any given base

// To return char for a value. For example '2'
// is returned for 2. 'A' is returned for 10. 
// 'B' for 11
function reVal($num)
{
    if ($num >= 0 && $num <= 9)
        return chr($num + ord('0'));
    else
        return chr($num - 10 + ord('A'));
}

// Utility function to reverse a string
function strev($str)
{
    $len = strlen($str);
    for ($i = 0; $i < $len / 2; $i++)
    {
        $temp = $str[$i];
        $str[$i] = $str[$len - $i - 1];
        $str[$len - $i - 1] = $temp;
    }
}

// Function to convert a given decimal 
// number to a base 'base' and
function fromDeci($res, $base, $inputNum)
{
    $index = 0; // Initialize index of result

    // Convert input number is given base 
    // by repeatedly dividing it by base 
    // and taking remainder
    while ($inputNum > 0)
    {
        $res.= reVal($inputNum % $base);
        $inputNum = (int)($inputNum / $base);
    }

    // Reverse the result
    $res = strrev($res);

    return $res;
}

// Driver Code
$inputNum = 282;
$base = 16;
$res = "";
print("Equivalent of $inputNum in base $base is " . 
                 fromDeci($res, $base, $inputNum));

// This code is contributed by mits 
?>

Output
Equivalent of 282 in base 16 is 11A

Time Complexity: O(logbasen) where 'n' is the input number and 'base' is the base to which the number is to be converted. 

Auxiliary Space: O(logbasen)

Method: Using int function

C++ 
#include <iostream>
#include <string>

using namespace std;

int main() {
    string n = "1100";
    int b = 2;
    int result = stoi(n, nullptr, b);
    cout << result << endl;
    return 0;
}
Java 
public class GFG {
    public static void main(String[] args) {
        String n = "1100";
        int b = 2;
        int result = Integer.parseInt(n, b);
        System.out.println(result);
    }
}
Python3 
n = "1100"
b = 2
print(int(n, b))
C# 
using System;

class Program {
    static void Main(string[] args) {
        string n = "1100";
        int b = 2;
        int result = Convert.ToInt32(n, b);
        Console.WriteLine(result);
    }
}
JavaScript 
const n = '1100';
const b = 2;
const result = parseInt(n, b);
console.log(result); // Output: 12

Output
12

Time complexity: O(N) Convert input number is given base by repeatedly inputNum dividing it by base and taking remainder takes O(n) complexity 

Auxiliary Space: O(1)

Comment
Article Tags:
Mathematical
DSA
base-conversion
Motlay

Explore