Data representation (part 3)

Activity Prompt:

Background

In this question, you will define BinaryToDouble, taking a single std::string value passed by const reference, and returning a double. The std::string will encode the floating point value in the same toy format as introduced in the lecture video, and your implementation of BinaryToDouble must return the floating point value it encodes. For example, the std::string below encodes the floating point value 3.5:

              Value (as char):        0    b    0    1    0    1    1    0    0
              Index (in std::string): 0    1    2    3    4    5    6    7    8
              Float Representation    -    -    Sign Exp. Exp. Man. Man. Man. Man.
    

Assignment Prompt

Your function must ensure the std::string passed to BinaryToDouble follows the format we specify, including the "0b" as the first two characters. The character in

• index 2 stores the sign bit,
• indices 3-4 store the exponent bits, and
• indices 5-8 store the mantissa bits.

Therefore, the characters in indices 2-8 must be either '0' or '1'. If the std::string fails to follow the format specified, your function must throw an std::invalid_argument exception. The exponent is encoded using a bias, so your final exponent must be calculated as an exponential field - bias, where bias is equal to 1.

Functions to Implement

    double BinaryToDouble(std::string bit_string);
    // BinaryToDouble(“0b0101100”) = 3.5
    // BinaryToDouble(“0b0000000”) = 0.0
    // BinaryToDouble(“0b1000000”) = -0.0