Convert from any base to decimal and vice versa

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. Value of A is 10, 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 below formula to convert from any base to decimal.

"str" is input number as string 
"base" is base of input number.

Decimal Equivalent is,
  1*str[len-1] + base*str[len-2] + (base)2*str[len-2] + ...

Below is implementation of above formula.

C++

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// 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-1]*base + str[len-1]*(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;
}

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Java

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// 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-1] *
    // base + str[len-1]*(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.

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Python3

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# 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-1]*base + str[len-1]*(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

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C#

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// 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-1] *
    // base + str[len-1]*(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.

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PHP

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<?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-1]*base + str[len-1]*(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
?>

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Output :



Decimal equivalent of 11A in base 16 is 282

 

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++

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// 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;
}

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Java

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// 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

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Python3

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# 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 

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C#

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// 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

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PHP

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<?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 
?>

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Output :

Equivalent of 282 in base 16 is  11A

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