Answer:
- 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 Positive
- By 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
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discrimination
