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Computer Systems

Computer Systems. Nat 4/5 Computing Science Lesson 2: More on Binary. REVISION. What is an integer? Convert 1100 1100 into a decimal number Convert 23 into binary. What are the three advantages of binary. ANSWERS. A whole number 1100 1100 = 204 23 = 0001 0111

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Computer Systems

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  1. Computer Systems Nat 4/5 Computing Science Lesson 2: More on Binary

  2. REVISION • What is an integer? • Convert 1100 1100 into a decimal number • Convert 23 into binary. • What are the three advantages of binary

  3. ANSWERS • A whole number • 1100 1100 = 204 • 23 = 0001 0111 • a) There are less rules of arithmetic. b) 0’s and 1’s are easier to represent. c) Any drop in voltage doesn’t effect data.

  4. Lesson Aims • By the end of this lesson you will be able to: • Describe what a real number is. • Describe what the mantissa is. • Describe what the exponent is. • Describe what Floating Point Representation is. • Represent real numbers using Floating Point representation. • State the storage terms used in computing.

  5. Nat 4/5 What is a real number? • Real numbers are ALL numbers both whole and fractional • Real numbers can be 1¾ or 1.75 or 1750 • Real numbers can be very very small 0.00000001 or very very large 1,987,897,564,859 • Real numbers can be very accurate 1245.235687412

  6. Nat 4/5 How are real numbers represented in binary • Real numbers are represented in binary using a system called floating point representation • It is similar to floating point notation that is used in decimal to represent very small very large numbers • For example 3*108= 300.000.000

  7. Nat 4/5 Floating point representation • In floating point notation, numbers can be divided into the base/mantissa/exponent • a*10b • “a” is the mantissa (the number) • 10 for the number system • “b” the exponent (raises 10 to the power of) • .183506*102 = 18.3506

  8. Nat 4/5 Floating point representation 214 = .214 * 1000 = .214*103 exponent mantissa base The point moves three places

  9. Nat 4/5 Floating point representation • The mantissa is the actual digits of the number • The exponent is the power (to which the base is raised) • In binary the base is always 2 • As the base is always 2 it can be ignored and all that has to be stored is, • The mantissa (the number)and the exponent (the power to which the base is raised)

  10. Nat 4/5 Floating point representation • 214 = 11010110 in binary • 11010110 = .11010110 * 21000 mantissa exponent base The point moves eight places

  11. Nat 4/5 Floating point representation • We can ignore the base and leave out the multiplication sign and write it as: • 110101101000 • It can also be written as 10110110 1000 exponent mantissa exponent mantissa

  12. Nat 4/5 Storage terms used in computing • A single unit in binary is a bit • A bit can be 1 or 0 • A binary number made up of eight bits is called a byte for example,11101101 • One Kilobyte is 1024 bytes, 1 Kb is one Kilobyte or 1024 bytes or 210 210 23 22 21 20

  13. Nat 4/5 Storage terms used in computing • 1 Kb = 1024 bytes • One Megabyte (Mb) = 1024 Kilobytes (220 bytes) • One Gigabyte (Gb) = 1024 Megabytes (230 bytes) • One Terabyte (Tb) = 1024 Gigabytes (240 bytes) • Sometimes the abbreviations are expressed in uppercase, KB, MB, GB and TB

  14. Nat 4/5 Storage terms used in computing Kilobyte Megabyte

  15. Nat 4/5 Gigabyte Megabyte

  16. Nat 4/5 Storage terms used in computing Kilobyte Megabyte Gigabyte Terabyte Petabyte Exabyte Zettabyte Yottabyte • A petabyte is the equivalent of 250 billion pages of text, enough to fill 20 million four-drawer filing cabinets.

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