1. Computer Systems Nat 4/5 Computing Science Data Representation
Lesson 2:
Floating Point Representation

2. REVISION What are two advantages of using the binary system?
Convert the number 56 into binary
Convert the following binary number into decimal:

3. ANSWERS Less rules of arithmetic Easy to represent two values
Voltage loss = no loss of data
56 =
= 204

4. Lesson Aims By the end of this lesson all pupils will be able to
List storage terms in ascending order:
Bit, Byte, Kilobyte, Megabyte, Gigabyte, Terabyte, Petabyte
Convert to and from bit->Petabyte

5. Lesson Aims – N5 By the end of this lesson all pupils will be able to
Describe what is meant by floating point representation
Use and explain the terms mantissa and exponent

6. Storage Terms Which is bigger, pennies or pounds?
Nat 4/5
Storage Terms
Which is bigger, pennies or pounds?
It is important to be able to sort terms into the correct order.
If buying a phone would you take a 512Mb version or a 4Gb version?
Why?

7. Higher up = bigger Storage Terms Petabyte (Pb) Terabyte (Tb)
Nat 4/5
Storage Terms
Petabyte (Pb)
Terabyte (Tb)
Gigabyte (Gb)
Megabyte (Mb)
Kilobyte (Kb)
Byte
Bit
x1024
x1024
x1024
x1024 x8
Higher up = bigger

8. Converting Between Terms
Nat 4/5
Converting Between Terms
If going from a smaller unit to a larger unit you divide.
If you wanted to know how many Megabytes were in 2048Kb then you would divide by 1024.
If you go to a smaller unit you should end up with more!

9. Converting Between Terms
Nat 4/5
Converting Between Terms
If going from a larger unit to a smaller unit you multiply.
If you wanted to know how many Gigabytes were in 5 TB then you would multiply by 1024.
If you go to a smaller unit you should end up with more of them!

10. What about the other numbers?
Nat 4/5
What about the other numbers?
So far we know how to store integers
These are whole Numbers
But what if we want to store real numbers
Numbers with decimal fractions
27.5 needs another way to represent it.
This method is called floating point representation

11. Floating Point Representation
Nat 4/5
Floating Point Representation
The structure of a floating point(real) number is as follows:
3.0 * 108
Only the mantissa and the exponent are stored. The base is implied (known already)
As it is not stored this will save memory capacity
Exponent
Mantissa
Base

12. Summary In ascending order
Nat 4/5
Summary
In ascending order
Bit, Byte, Kilobyte, Megabyte, Gigabyte, Terabyte, Petabyte
8 bits in a byte
1024 KB = 1 MB and so on…
Floating point representation is used to represent Real numbers
That is numbers with a decimal portion