# Binary to Decimal conversion in C++

This tutorial would help in learning the following:

• Conversion of numbers from binary to decimal in C++.
• Re-conversion of characters into their respective ASCII codes
• Code for Binary to Decimal conversion in C++

The decimal number system uses all the 10 digits (0 to 9) to represent a number while the binary number system 0 and 1. The following algorithm is used to convert a binary-number to a decimal-number:

let the binary number be 111111

1. Give proper index to each digit of the binary number, starting with zero and from the rightmost digit
number->111111
index—->543210
2. multiply the number present at index ‘i’ with the ith power of  2
index 0 -> 1* 20 = 1
index 1 -> 1* 21 = 2
index 2 -> 1* 22 = 4
index 3 -> 1* 23 = 8
index 4 -> 1* 24 = 16
index 5 -> 1* 25 = 32
3. add all the products obtained from step 2, to get the equivalent decimal number
1 + 2 + 4 + 8 + 16 + 32 = 63
(111111)2 ~ (63)10

Each character used in computing is assigned a special ASCII code (decimal-number-system); hence, once a binary code is converted to its equivalent decimal-number code, the latter can be assigned a character as per the ASCII convention.
Note, there can be different encoding systems on different machines.

## C++ program  to convert binary to decimal

```//Note, this program assumes the convention of giving a fullstop after the octal-code for an individual character
#include <stdio.h>
#include <math.h>//this contains function pow which will be used to calculate the powers of 2
#define binarystring "1000011.1101111.1100100.1100101.100000.1010011.1110000.1100101.1100101.1100100.1111001."
#define max 10//assuming that the length of individual code for a character will not exceed 10
char binary(char array[])
{
char code=0;//the sum of products, as explained in the algorithm, would be stored in this variable
char c;
int temporary;
int i;
int j=0;
for(i=0;array[i]!='\0';i++);
//obtaining the index of the last code-character in array[]
for(--i;i>=0;i--){
c=array[i];
temporary = c - '0';
code+=temporary*pow(2,j++);
}
return code;//since the integer sum is returned in a character variable, the corresponding character for the integer code would be assumed
}
void binaryToString(char array[])
{
char helper[max+1];//extra length to accommodate the null character
int index = 0;
for(int i=0;array[i]!='\0';i++){
if(array[i]=='.')//printing the value of the code for one character
{
helper[index]='\0';
printf("%c",binary(helper));
index=0;
}
else//stacking up the incomplete code for one character
{
helper[index++]=array[i];
}
}
}
int main()
{
printf("\nThe original form of the binary code %s is: ",binarystring);
binaryToString(binarystring);
return 0;
}```

Output:

`The original form of the binary code 1000011.1101111.1100100.1100101.100000.1010011.1110000.1100101.1100101.1100100.1111001. is: Code Speedy`

Summary:

#### char binary(char[]):

• the index of the last character in array[] is stored in ‘i’
• the value of ‘j’ corresponds with the required power of 2 that is required for the character at given index ‘i’
• the numerical value of the character-code at index ‘i’ is stored in ‘temporary’
• the sum of products for different indices is stored in ‘code’
• value of ‘code’ is returned

#### void binaryToString(char[])

• helper[] stores the binary code for one character at a time
• binary(char[]) is called and helper[] is passed to it to print the corresponding character for the binary code in helper[]