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

1.What are two advantages of using the binary system? 2.Convert the number 56 into binary 3.Convert the following binary number into decimal:

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

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

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

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? Nat 4/5

Storage Terms Petabyte (Pb) Terabyte (Tb) Gigabyte (Gb) Megabyte (Mb) Kilobyte (Kb) Byte Bit Nat 4/5 x1024 x8 x1024

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  If you go to a smaller unit you should end up with more! 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  If you go to a smaller unit you should end up with more of them! 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 Nat 4/5

Floating Point Representation  The structure of a floating point(real) number is as follows:  3.0 * 10 8 implied  Only the mantissa and the exponent are stored. The base is implied (known already)  As it is not stored this will save memory capacity Nat 4/5 Mantissa Base Exponent

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 Nat 4/5