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

REVISION What are two advantages of using the binary system? Convert the number 56 into binary Convert the following binary number into decimal: 1100 1100

ANSWERS Less rules of arithmetic Easy to represent two values Voltage loss = no loss of data 56 = 0011 1000 1100 1100 = 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? 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?

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

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!

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!

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

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

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