DECIMAL_FLOAT_TO_IEEE754_FP.cpp

#include <iostream>
#include <cmath>
#include <tuple>
#include <ctime>
#include <algorithm>
using namespace std;
#define BIAS 7
//no of test cases
#define CASE_AMOUNT 30

//range of values
#define LO -255
#define HI 255

#define NUM_SYS 2

//decimal places
#define PRECISION 5

//converts a decimal int to binary
string binar(int dig)
{
    string bin = ""; int rem;
    while(dig)
    {
        rem = dig%NUM_SYS; dig/=2;
        bin.append(to_string(rem));
    }
    reverse(bin.begin(), bin.end());
    return bin;
}

//converts a decimal float to binary string
//eg. 4.25 to 100.01
tuple<string, string, string> f_to_b(float f)
{
	//finding sign of input f
    int sgn = 0;
    if(abs(f)!=f && f!=0.0) sgn = 1;
    string sign = to_string(sgn);
	
	///get binary of the int part of the float
	//if 4.25, this would get binary of 4 only
    string bin = binar(abs(int(f)));

	//split into two using the dot, take the part after the point
	//eg 0.25 in 4.25
    string d_str = to_string(abs(f));
    if(d_str.find(".")<d_str.length()) d_str = d_str.substr(d_str.find("."));
    
	//takes dp upto precision
	if(d_str.length()-1>PRECISION) d_str = d_str.substr(0, PRECISION+1);
	
	//converts 0.25 back to float for calculations
    float a_dec = stof(d_str); d_str = "";

	//0.25 to binary
    while(!(a_dec<(1.0/pow(10, PRECISION)))) ///while a is not small enough (can't be perfectly zero)
    {
		//appending ans to empty string d_str
        a_dec *= 2;
        d_str.append(to_string(int(a_dec)));
        a_dec = a_dec - float(int(a_dec));
    }
	
	//return 4.25's binary 100.01
	//like make_tuple(100, 01, 0);
    return make_tuple(bin, d_str, sign);
}


tuple<string, int> pop_zeroes(string bin_l)
{
    int i = 11, expbase = 0;
	
	//while zeroes, remove em and decrease exponent
    while(i--)
    {
        if(bin_l.at(0) == '0')
        {
            bin_l = bin_l.substr(1);
            expbase--;
        }else break;

        if(i==0)
            return make_tuple("0", 0);
    }
    if(bin_l.length()>1) bin_l = bin_l.substr(1);
    expbase--;
    return make_tuple(bin_l, (expbase+BIAS));
}


//binary float eg 100.01 to IEEE standard
///bin_f is part before binary point, bin_l is after, sgn is sign
string standardize(string bin_f, string bin_l, string sgn)
{
    string bin = ""; int exp;
	
	//eg if input == 100.01, i.e. bin_f = 100
    if(bin_f.length()>1)
    {
        exp = bin_f.length()-1+BIAS;
        bin = bin_f.substr(1) + bin_l;
        if(bin.length()>11) bin = bin.substr(0, 11);
        return sgn+" "+binar(exp)+" "+bin; //bin is bin_f+bin_l
    }

	//eg if input == 0.01, i.e. bin_f is null
    if(bin_f.empty())
    {
        tie(bin_l, exp) = pop_zeroes(bin_l); //removes the zeroes and decreases exponent
        return sgn+" "+binar(exp)+" "+bin_l;
    }
	
	//else exp is zero, bin_f.len = 1
	//eg binary of 1.5 aka 1.1
    return sgn + " " + binar(BIAS) + " " +bin_l;
}

int main(void){

    float inp1, inp2, ans;
    string bin_f, bin_l, exp;


        cin >> inp1 >> inp2;
        ans = inp1 + inp2;


        tie(bin_f, bin_l, exp) = f_to_b(inp1);
        cout << inp1 << " : " << standardize(bin_f, bin_l, exp) <<endl;

        tie(bin_f, bin_l, exp) = f_to_b(inp2);
        cout << inp2 << " : " << standardize(bin_f, bin_l, exp) <<endl;

        tie(bin_f, bin_l, exp) = f_to_b(ans);
        cout << ans << " : " << standardize(bin_f, bin_l, exp) <<endl<<endl<<endl;

    return 0;
}