Error with converting a binary input from the user into a double value

Question

so below I've written code to convert a binary value into its double equivalent. However,

binConversionDouble("0111111111111111111111111111111111111111111111111111111111111111")

gives:

179769313486149841153851976955417028335471708986564534469802644816832731470450734933617524554272984142853535521554773891036051644209223511432842829043130247900910146729889177843938143131935935774382721844130004287345894163215696051477671359689698349651554878795894806567601614971014045300870721438977577975808.000000

but the actual value of DBL_MAX is:

179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368.000000

My logic seems to be correct however I am unsure whether the above is a case of loss of precision in arithmetical calculations or a flaw in my logic. Can someone please guide me as to why the two values are different?

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>
#include <assert.h>
#include <limits.h>
#include <math.h>
#include <float.h>

double binConvertDouble(const double *mainBinArr, const char usersBinVal[]) {

    double isNegative = 1;
    if (usersBinVal[0] == '1') {isNegative = -1;}

    double exponent = 0;
    char exponentSubString[12];
    int count = 0;
    for(int i =0; i<11; i++) {
        exponentSubString[i] = usersBinVal[i+1];
        count = count + 1;
    }
    exponentSubString[11] = '\0';
    exponent = calculatingDoublesExp(mainBinArr, exponentSubString);

    double summingMantissa = 0;
    for(int i =12; i<52; i++) {
        if (usersBinVal[i] == '1') {
            summingMantissa = summingMantissa + pow(2, 11-i);
        }
    }
    double totalMantissaVal = 0;
    totalMantissaVal = 1 + summingMantissa;
    double actualExp = pow(2, (exponent-1023));
    double finalVal = isNegative * totalMantissaVal * actualExp;
    return finalVal;
}


int main() {
  printf("VALUE WE GET %f\n", binConversionDouble("0111111111111111111111111111111111111111111111111111111111111111"));
return 0;
}

Answer 1

The example input string "0111111111111111111111111111111111111111111111111111111111111111" corresponds to an IEEE-754 double NaN (Not-a-Number) value. The exponent part of the string is "11111111111" corresponding to a (radix-2) exponent of 1024 plus the zero-offset bias of 1023. However the maximum (radix-2) exponent of an IEEE-754 finite, numeric value is 1023. The out-of-range exponent causes pow(2, exponent-1023) to return inf when exponent is 2047 (exponent includes the zero-offset of 1023 here).

The IEEE-754 DBL_MAX value is represented by the input string "0111111111101111111111111111111111111111111111111111111111111111".

The code that extracts the significand (mantissa) value from the input string is terminating too early:

    double summingMantissa = 0;
    for(int i =12; i<52; i++) {
        if (usersBinVal[i] == '1') {
            summingMantissa = summingMantissa + pow(2, 11-i);
        }
    }

The terminating condition should be i<64.