Question

I'm trying to convert between different number representations in C++ , I have the prototype but im not sure what do do from here

bool convertF(double & x, const string & bits);

bits is supposed to be an 8-bit (not 5-bit) value, each char being '0' or '1'; if not, return

false. The first bit of bits represents the sign bit, the next 3 bits represent the exponent,

and the next 4 bits represent the significand.

convertF may assume without checking that the 3 exponent bits are not all the same.

convertF's job is to set x to the floating-point number that bits represents and return

true.

For example, convertF(x, "101011000") should set x to -7/8 == -0.875

Answer 1

double helper(double a){
  
   string aString = to_string(a);
   int decimalPlace=aString.length();
   for(int i=0;i<aString.length();i++){
       if(aString[i]=='.'){
           decimalPlace = i;
           break;
       }
   }
   double ans = 0;
   double p = 1;
   for(int i=decimalPlace-1;i>=0;i--){
       if(aString[i]=='1')
           ans+=p;
       p = p*2;
   }
   p = 0.5;
   for(int i=decimalPlace+1;i<aString.length();i++){
       if(aString[i]=='1')
           ans+=p;
       p = p/2.0;
   }
   return ans;
}

bool convertF(double &x, const string & bits){

   if(bits.length()==8){
       for(int i=0;i<8;i++){
           if(bits[i]=='0' || bits[i]=='1')continue;
           else return false;
       }
       bool isPositive = true;
       if(bits[0]==1)isPositive = false;
       string exponent = bits[1]+bits[2]+bits[3];
       int valExp = binaryOf(exponent)-3;
       double mantissa = 0.0;
       if(bits[4]){
           mantissa+=0.1;      
       }
       if(bits[5]){
           mantissa+=0.01;
       }  
       if(bits[6]){
           mantissa+=0.001;
       }
       if(bits[7]){
           mantissa+=0.0001;
       }
       double val = 1.0;
       val+=mantissa;
       val = val*power(10,valExp);
       x = helper(val);

       if(!isPositive)x = x*(-1);
       return true;
   }
       return false;
}

The above is a complete implementation for given an 8 bit floating point representation , to find the floating point number . In the above code , two functions have been considered that they can be easily computed namely binaryOf() which takes in as input a string and finds the corresponding decimal value , and power() which calculates x^y even when y is negative.These two functions can be easily implemented but if difficulty is encountered,then do comment.