C Program to find the floating point IEEE 754 representation

A computer can use only two kinds of values. That is, fixed point and floating point. The fixed point values are stored in the computer memory in binary format representing their ASCII value.

For example:-

Character ‘A’ can be stored as- 1000001. Because, 65 is ASCII value of ‘a’. In case of floating point values, these follow the IEEE 754 standard to store in memory. Whenever any programming language declared- float a; Then the variable 'a's value will be stored in memory by following IEEE 754 standard.

This standard specifies the single precision and double precision format. In case of C, C++ and Java, float and double data types specify the single and double precision which requires 32 bits (4-bytes) and 64 bits (8-bytes) respectively to store the data.

Lets have a look at these precision formats.

Single Precision:-

It requires 32 bit to store. Following is the format of single precision.

In order to store a float value in computer memory, a specified algorithm is followed.

Take an example at float value- 3948.125

1. Covert 3948 to binary. i.e. 111101101100
2. Convert .125 to binary,

         0.125 x 2 = 0.25    0

         0.25 x 2 = 0.5        0

        0.5 x 2 = 1             1

            = 0.001

Now 3948.125 = 111101101100.001

3. Normalize the number so that the decimal point will be placed after MSB-1. i.e.

111101101100.001 = 1.11101101100001 x 2¹¹

4. Now, for this number s=0, as the number is positive.

Exponent' = 11 and

Mantissa = 11101101100001

5. Bias for single precision used is 127 so,

Final exponent = exponent' + 127 i.e.

E= 11 + 127= 138 = 10001010 in binary.

6. Final value-

In this format the number 3948.125 will be stored in main memory.

For double precision values following changes are expected:

Total bits required – 64

Exponent – 11 bits

Mantissa – 52 bits

Bias value – 1023

Now, if you want to find the IEEE 754 representation at any floating point number, following program can be used.

#include<stdio.h>

int binary(int n, int i)

{

    int k;

    for (i--; i >= 0; i--)

   {

      k = n >> i;

      if (k & 1)

          printf("1");

      else

         printf("0");

    }

}

typedef union

{

      float f;

      struct

      {

            unsigned int mantissa : 23;

            unsigned int exponent : 8;

            unsigned int sign : 1;

       } field;

} myfloat;

int main()

{

           myfloat var;

    printf("Enter any float number: ");

           scanf("%f",&var.f);

           printf("%d ",var.field.sign);

           binary(var.field.exponent, 8);

           printf(" ");

           binary(var.field.mantissa, 23);

           printf("\n");

           return 0;

}

Explanation-

The function binary( ) is used to convert the number ‘n’ into binary format and print its ‘i’ number of bits.

In C, structure members can be specified with no. of bits with size. It is known as bit fields. As ‘float f’ is declared in ‘union myfloat’. It can use 23 bits to store mantissa exponent can use 8 and sign can use one! The variable ‘var’ is at myfloat type. So, in order to access mantissa, we can use ‘var.field. mantissa’. Here, mantissa is the name of internal structure. So, float value’s internal bits can be accessed bitwise with sign, exponent and mantissa separately.

Run the program and see the output of the said example!

Giving brain to Computer

If someone has told you to create a brain, what will you do first? Is that so simple? Obviously not! If you want to create something that will coordinate the activities of the system will be a complicated task ever seen. The reason I wrote here that all we know the real brain of computer is a microprocessor. It is the most complicated part of the computer system. The logic behind computer system is in-built inside the microprocessor. Future engineers learn this logic in computer architecture but very few understand that.

The concept of giving brain to the computer system is basically originated by Jon Von Neumann in the mid of 20^th century. So he is well known as father of modern computer. The second person who is known as father of modern computing is Allen Turing. Before 1950, the computer and its parts were working independently as per their own different control. This was the reason why there was no coordination among these all parts of the computer system. How our human body works? None of the part of the human body has its own control mechanism. The overall coordination and control is given by human brain. Due to this, human body has a great coordination among all the parts of it. For example: we cannot keep our noses close continuously by putting our hands on it. It is just impossible! Just try it…!!! You can’t do that. This is only due to the coordination fetched inside the body and controlled by the brain. The same concept is adopted and applied to create a computer of new generation. Still today our computers work on this concept. The brain here is well known as Central Processing Unit or in short a CPU. We generally call it by microprocessor or just as processor. Neumann is the originator of this concept. He has shaped the idea of the computer is more specific manner. He is the real pioneer in the research of computing field.

He has not only given the design of the modern computer but also given the logic behind various activities that computer system does. Such as, computational, arithmetical, logical or data transfer activities. I always used to say that computer is not a magical machine it is a logical machine. At least engineers should have to think in this way. When the brain is given to the computer in the history its working efficiency was increased dramatically. Computer scientists made several necessary changes in the design of this brain. Today, we are seeing most advanced brains of the computer that is microprocessor. From the generation of 4 bit 4004 processor, we are now in multi-core generations and approaching towards optical and Nano processors. This is just the advancement of the generations.

This blog gives the look of these new technologies of the computing world including a ‘different’ brain of the computer that is ‘microcontroller’. When minimized tasks of the computer are required, this brain (generally small body) is used to drive the computer system. This blog will focus various aspects of microprocessor and microcontrollers used in the computing world today. Hope you will like that.