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Write a recursive function (with no loops or static variables) named binToDec that takes a string object as a parameter. The string will consist of 1s and 0s, representing a binary number. The function should return an int giving the decimal equivalent. For example,
cout << binToDec("101010") << endl;
should print out 42.
We can calculate this conversion as 1*25 + 0*24 + 1*23 + 0*22 + 1*21 + 0*20. This is, incidentally, the same as how decimal numbers work, except the base is different. For example “1027” is 1*103 + 0*102 + 2*101 + 7*100.
Notice that the indices of the characters count in the opposite direction as the exponents do.
You may not use any built-in base-conversion functionality of C++.
You may write a helper function that meets the specifications and calls your recursive function with additional arguments.
You may use the string::substr() function if you want.
Expert Answer
Answer:
#include<iostream>
#include<stdlib.h> /* header file for atoi() and itoa() functions */
#include<cmath> /* header file for pow() function */
using namespace std;
int decimal,weight; /* global variables, all the global variables have the initial value zero(0), so decimal=0, weight=0 */
int binToDec(char number[10]) /* function definition starts here, and it is taking a string as its argument and returns an integer */
{
int bit,n; /* local variables */
char n1[10]; /* local variable */
n=atoi(number); /* converts the string to number and storing in n */
if(n>0) /* if n is greater than 0 */
{
bit=n%10; /* identifying the right most digit */
decimal=decimal+bit*pow(2,weight); /* calculating the partial sum (by multiplying the digit with its position value in binary) */
n=n/10; /* updating the number by dividing with 10 */
weight++; /* incrementing the weight value */
itoa(n,n1,10); /* converting the integer n to string and storing in n1, 10 is the base of the number system */
binToDec(n1); /* recursive call to binToDec() */
}
else return decimal; /* returning the value of decimal to the main() function */
}
int main() /* main() function definition */
{
char number[10]; /* string declaration */
cout<<“Enter a binary number:”;
cin>>number; /* taking a binary number into number */
cout<<“The equivalent decimal number is:”<<binToDec(number); /* function call to binToDec() */
return 0;
}
Output:
