Create a design document for a program that will take a number from the user and convert it to IEEE single precision format. The program displays the IEEE representation (Single precision) of the number entered by the user.
PLEASE ADD THE PSEUDOCODE AND CODE WITH C PROGRAMMING
Pseudocode:
All sections have been commented appropriately in regards to the explanation.
The entire process takes advantage of how the union data type works. Since the values stored in each of the members is the same as the first member of the union, the first member to be declared is the float number that we give as the input.
As for the Union data type, the ordering of the declaration is also important due to how the program assigns the values from the float to the unsigned integers. Since the size of the struct ieee is 32 bits, float is also taken as 32 bits. The values are then converted and stored by the program starting from LSB to MSB and distributed across the 3 sub members of res, namely significand, exponent and sign.
Code:
#include<stdio.h>
void printBinary(int n, int i)
{
int k;
int cur_digit;
for (k = i - 1; k >= 0; k--) {
cur_digit=n>>k;
if (cur_digit & 1)
printf("1");
else
printf("0");
}
/*NOTE: WE USE BITWISE OPERATORS HERE AS SINCE BITWISE OPERATORS
OPERATE ON BIT VALUES ONLY IT SAVES US THE TROUBLE
OF TRYING TO MANUALLY CONVERT, THEY GET CONVERTED
AUTOMATICALLY*/
/*PRINTBINARY HERE RIGHT SHIFTS AND THEN PERFORMS BITWISE AND
OPERATION STARTING FROM THE MSB
HERE SMALL i REPRESENTS THE NUMBER OF BITS UNTIL WHICH WE WANT TO
PRINT THE BINARY NUMBER TO
>> IS THE A BINARY RIGHT SHIFT OPERATOR WHICH SHIFTS THE
FIRST OPERAND TO THE RIGHT BY NUMBER OF
DIGITS SPECIFIED BY THE SECOND OPERAND.SINCE i IS THE SIZE OF THE
NUMBER ITSELF, SHIFTING BY i-1
GIVES US THE MSB OF THE NUMBER WHOSE BINARY REPRESENTATION WE ARE
TRYING TO GET. THE OPERATOR &
IS ALSO A BITWISE OPERATOR, HERE THE cur_digit STORES THE BITWISE
VALUES STARTING FROM MSB TO LSB.
PERFORMING & OPERATION WITH IT GIVES US "1" WHEN THE BIT VALUE
WAS 1 ELSE "0", THUS PRINTING THE BIT VALUES OF
THE INPUT NUMBER ONE BY ONE STARTING FROM MSB TO LSB*/
printf("|");
}
/*MEMBERS OF UNION SHARE MEMORY AND STORE SAME VALUES, AND THE SIZE
OF THE UNION IS THE SAME AS THE SIZE OF THE LARGEST MEMBERS
HERE THE LARGEST MEMBER IS THE STRUCT IEEE THAT IS A TOTAL OF 32
BITS; AS FOR TYPEDEF, THE SYNTAX IS
TYPEDEF <ACTUAL DATA TYPE> <DERIVED DATA TYPE NAME (GIVEN
BY USER)>, HERE num IS THE NAME OF THE UNION DATA TYPE, ORDERING
IS IMPORTANT AND IS STORED
FROM LSB TO MSB*/
typedef union{
float real;
struct ieee{
unsigned int significand : 23;//we
use bit fields when we know maximum bits that will be used,
significand has 23 bits
unsigned int exponent :
8;/*exponent has 8 bits, and the exponent stored here is the biased
exponent.
Bias value is defined as (2^n)-1
for n bits, so it is +127 of true exponent value*/
unsigned int sign : 1;//sign only
requires 1 bit
/*here the values that actually get
sored in significand, exponent, and sign are already the values
that correspond to the ieee format due
them sharing the same memory, now
as C will only output the numbers in decimal, that is base 10, all
we need to do is output the binary
equivalent stored at these
places*/
}res;
}num;
void getIEEE(num in)
{
printf("|%d|",in.res.sign);//as sign bit is only a single digit we
can directly print it out
printBinary(in.res.exponent,8);
printBinary(in.res.significand,23);
//we need to convert exponent and significand to their binary
equivalents
printf("\n");
}
int main()
{
num in;//stores the input and the result
printf("Enter real number :");
scanf("%f",&in.real);
printf("Decimal equivalents of the number stored in
memory are :\n");
printf("Significand :%u\n",in.res.significand);
printf("Exponent :%u\n",in.res.exponent);
printf("Sign :%u\n",in.res.sign);
printf("IEEE754 form of %f is :\n",in.real);
getIEEE(in);
return 0;
}
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