1. Normalised Floating Point Numbers
Normalised Floating Point Binary Numbers – accurate data representation using a specificed format

2. Question 1 Represent +1.5 in the following format:
4 bits for the mantissa
4 bits for the exponent
In Normalised format

3. Required Format =
Mantissa
Exponent

4. In order for it to be Normalised1
The POINT needs to go between the first two bits AND…
Mantissa
Exponent

5. In order for it to be Normalised2
Both bits need to be different. E.g. 10 or 01 (not 11 or 00)
Mantissa
Exponent

6. 0.110 1.1 Step 2 Step 1 CONVERT THE NUMBER INTO BINARY
What would it look like if normalised?
0.110
1.1

7. 0.110 1.1 Step 3 How many places has the decimal moved? (note to
Get it from its NORMALISED FORM BACK TO ORIGINAL?)
0.110
1.1
ORIGINAL
NORMALISED

8. 0.110 1.1 Step 3 How many places has the decimal moved? (note to
Get it from its NORMALISED FORM BACK TO ORIGINAL?)
0.110
1.1
ORIGINAL
NORMALISED

9. Step 4
Create the exponent (how many places to the right or left!)
0.110
0001
MANTISSA
EXPONENT

10. +1.5 =
0.110
0001
MANTISSA
EXPONENT

11. Question 2 Represent -6 in the following format:
4 bits for the mantissa
4 bits for the exponent
In Normalised format

12. Required Format =
Mantissa
Exponent

13. In order for it to be Normalised1
The POINT needs to go between the first two bits AND…
Mantissa
Exponent

14. In order for it to be Normalised2
Both bits need to be different. E.g. 10 or 01 (not 11 or 00)
Mantissa
Exponent

15. 1010. 1.010 Step 2 Step 1 CONVERT THE NUMBER INTO BINARY
What would it look like if normalised?
1010.
1.010

16. 1.010 1010. Step 3 How many places has the decimal moved? (note to
Get it from its NORMALISED FORM BACK TO ORIGINAL?)
1.010
1010.
Always do your calculations to find the exponent on the NORMALISED number. Move the point where it would be in the original and that gives you your exponent!
ORIGINAL
NORMALISED

17. 1.010 1010 Step 3 How many places has the decimal moved? (note to
Get it from its NORMALISED FORM BACK TO ORIGINAL?)
1.010
1010
ORIGINAL
NORMALISED
ALWAYS DO YOUR CALCULATION OF THE EXPONENT FROM THE NORMALISED NUMBER. MOVE THE POINT TO THE ORIGINAL PLACE AND MAKE NOTE OF Number and left or right

18. Step 4
Create the exponent (how many places to the right or left!) +3
1010.
0011
MANTISSA
EXPONENT

19. -6 =
1010
0011
MANTISSA
EXPONENT

20. Example A Level Questions
PAST PAPER A LEVEL QUESTION AND ANSWERS
Taken with permission from OCR Exam Board

25. Example A Level Questions
For when you have a 16 bit number where the mantissa is 10bits and the exponent is 6 bits: 
the largest positive number will be:
Mantissa: Exponent:
the smallest positive number will be:
Mantissa: Exponent:
the largest negative number will be:
Mantissa: Exponent:
the smallest negative number will be:
Mantissa: Exponent: ? ? ? ? ? ? ? ?

26. June 2010

30. Using 5=Mantissa 3 = Exponent
Spot the careless mistake