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

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

Required Format = Mantissa Exponent

In order for it to be Normalised 1 The POINT needs to go between the first two bits AND… Mantissa Exponent

In order for it to be Normalised 2 Both bits need to be different. E.g. 10 or 01 (not 11 or 00) Mantissa Exponent

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

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

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

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

+1.5 = 0.110 0001 MANTISSA EXPONENT

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

Required Format = Mantissa Exponent

In order for it to be Normalised 1 The POINT needs to go between the first two bits AND… Mantissa Exponent

In order for it to be Normalised 2 Both bits need to be different. E.g. 10 or 01 (not 11 or 00) Mantissa Exponent

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

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

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

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

-6 = 1010 0011 MANTISSA EXPONENT

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

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: 0.111111111 Exponent: 011111 the smallest positive number will be: Mantissa: 0.000000001 Exponent: 100000 the largest negative number will be: Mantissa: 1.000000000 Exponent: 011111 the smallest negative number will be: Mantissa: 1.111111111 Exponent: 100000 ? ? ? ? ? ? ? ?

June 2010

Using 5=Mantissa 3 = Exponent Spot the careless mistake