Question

In a language of your own choosing, write a computer program that takes as input a decimal (base 10) floating point number, and converts this number into a binary floating-point representation. The binary floating-point representation should consist of 1 bit for the sign of the significand; 8 bits for the biased exponent; and 23 bits for the significand. In addition to program source code, provide a screenshot showing the tasks identified below.

1. Provide an output that shows your input decimal floating-point values.

2. Demonstrate that your program works in the following input cases by showing the output in the form of 32 bits including sign bit, biased exponent, and significand:

1. 1. Small exponent value.
   2. Large exponent value.
   3. Negative exponent value.
2. 4. Negative significand.

Answer 1

// C program to convert a real value

// to floating point representaion

  

#include <stdio.h>

  

void printBinary(int n, int i)

{

  

    // Prints the binary representation

    // of a number n up to i-bits.

    int k;

    for (k = i - 1; k >= 0; k--) {

  

        if ((n >> k) & 1)

            printf("1");

        else

            printf("0");

    }

}

  

typedef union {

  

    float f;

    struct

    {

  

        // Order is important.

        // Here the members of the union data structure

        // use the same memory (32 bits).

        // The ordering is taken

        // from the LSB to the MSB.

        unsigned int mantissa : 23;

        unsigned int exponent : 8;

        unsigned int sign : 1;

  

    } raw;

} myfloat;

  

// Function to convert real value

// to IEEE foating point representation

void printIEEE(myfloat var)

{

  

    // Prints the IEEE 754 representation

    // of a float value (32 bits)

  

    printf("%d | ", var.raw.sign);

    printBinary(var.raw.exponent, 8);

    printf(" | ");

    printBinary(var.raw.mantissa, 23);

    printf("\n");

}

  

// Driver Code

int main()

{

  

    // Instantiate the union

    myfloat var;

  

    // Get the real value

    var.f = -2.25;

  

    // Get the IEEE floating point representation

    printf("IEEE 754 representation of %f is : \n",

           var.f);

    printIEEE(var);

  

    return 0;

}