Pseudocode of creating a program to convert to IEEE 754 to a real number

Step1: Check If the number is Positive or Negative.  Step2: If it is positive then save the sign of it as 0.  Step3: If it is negative then save the sign of it as 1. Step4: Covert the negative number to Positive. Step5: Convert the IEEE 754 to Binary. Step6: convert the integer part into binary form  Step7: Convert fractional part into binary form Step8: To convert Integer part, Devide the number by 2 and note down the reminder and Keep deviding unless dividend is less than 2 Step9: copy all the reminders together Step10: Multiply decimal part by 2 unless fractional part is 0. Step11: By noting down integral part, keep multiplying decimal part by new value of 2 untill perfect number is reached. Step6: Find the Mantissa. Step7: Concatinate the Sign, exponent and the mantissa.

Explanation:

For Example : 20.75

First step (converting 50 (in base 10) to binary):

No is PositiveBy dividing 20 by 2, which gives 10 with no remainder 0. Now Devide 10 by 2, which gives 5 with a remainder of 0. Now Devide 5 by 2, which gives 2 the reminder as 1 Now Devide 2 by 2, which gives 1 with reminder as 0 Now devide 1 by 2, which gives 0 with reminder as 1 We read the result from bottom to top  which is 10100

Second part is to convert 0.75 to binary:

We have to multiply 0.75 by 2, which gives 1.5. We keep only the integer part, which is 1.  Now, we do 1.5 - 1, which gives 0.5. Now, We multiply 0.5 by 2, which gives 1.   Now we do 1 - 1, which gives 0. Reading from Top to bottom will give 110

Final Answer is : 10100.110