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Computer Systems

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

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Computer Systems

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  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: 1100 1100 • Write -23 in binary using 8 bit twos complement. • Write 6.75 in binary.

  3. ANSWERS • Less rules of arithmetic • Easy to represent two values • Voltage loss = no loss of data • 56 = 0011 1000 • 1100 1100 = 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. 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. Nat 4/5 Storage Terms x1024 x1024 x1024 x1024 x1024 Link to web site with memory comparisons x8 Higher up = bigger

  8. Nat 4/5 Converting Between Terms • If going from a smaller unit to a larger unit you divide. • Example: Going from KB to MB • If you wanted to know how many Megabytes (larger) were in 2048KB (smaller) then you would divide2048KB by 1024. • 2048KB / 1024 = 2GB. • If you go to a larger unit you should end up with a smaller number!

  9. Nat 4/5 Converting Between Terms • If going from a larger unit to a smaller unit you multiply. • Example: Going from TB to GB • If you wanted to know how many Gigabytes were in 5 TB then you would multiply by 1024. • 5TB * 1024 = 5,120GB. • If you go to a smaller unit you should end up with more of them! N4: Complete Q1 – 5 of Worksheet 2 N5: Complete Q1 – 8 of Worksheet 2

  10. 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 realnumbers • These are numbers with decimal fractions e.g. 0.5 or 1.2597 or 27.5 • 27.5 needs another way to represent it. • This method is called floating point representation • It is very similar to Standard Notation use in your Maths class.

  11. 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 Base Mantissa

  12. 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 Realnumbers • This includes numbers with a decimal portion N5: Complete Q9 – 12 of Worksheet 2

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