Write a C++ program using recursion to convert a number in binary (from 1 to 10) to a decimal number. The algorithm states that each successive digit in the number is multiplied by the base (2) raised to the power corresponding to its position in the number. The low-order digit is in position 0. We sum together all of these products to get the decimal value. For example, if we have the binary number 111001, we convert it to decimal as follows:
1 * 20 = 1
0 * 21 = 0
0 * 22 = 0
1 * 23 = 8
1 * 24 = 16
1 * 25= 32
Decimal value = 1 + 0 + 0 + 8 +16+ 32 = 57
A recursive formulation of this algorithm can extract each digit and compute the corresponding power of the base by which to multiply. Once the base case (the last digit is extracted), the function can sum the products as it returns.
In C++ we can represent a binary number using integers. However, there is a danger—the user can enter an invalid number by typing a digit that’s unrepresentable in the base. For example, the number 1011201 is an invalid binary number because 2 isn’t allowed in the binary number system. Your program should check for invalid digits as they are extracted, handle the error in an appropriate way (that is, it shouldn’t output a numerical result), and provide an informative error message to the user.
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