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Computer Systems

In this lesson, students will explore the concept of floating point representation and its significance in data representation. They'll learn about the advantages of the binary number system, convert decimal numbers to binary, and vice versa. Key storage terms will be listed in ascending order, including bit, byte, kilobyte, and terabyte. The lesson emphasizes how floating point representation allows the storage of real numbers with decimal fractions, providing more efficient memory usage. By the end, students will be able to describe and explain mantissa and exponent terms.

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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

  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 x8 Higher up = bigger

  8. 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. 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. 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 • Numbers with decimal fractions • 27.5 needs another way to represent it. • This method is called floating point representation

  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 • That is numbers with a decimal portion

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