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1.1 Data Representation

1.1 Data Representation. ASCII, Binary <-> Denary Conversion, Integer & Boolean data types. Learning Objectives:. Describe ASCII as character format data type and explain the use of this code. Describe the binary number system. Convert simple numbers between denary and binary.

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1.1 Data Representation

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  1. 1.1 Data Representation ASCII, Binary <-> Denary Conversion, Integer & Boolean data types

  2. Learning Objectives: • Describe ASCII as character format data type and explain the use of this code. • Describe the binary number system. • Convert simple numbers between denary and binary.

  3. The Binary System • Computers store information (data of all types – numbers, characters, sound, pictures, …) in Binary format i.e. base 2. • i.e. 0 or 1 • Used because computers can only store and understand 2 states: • i.e. whether a circuit has current flowing or not / circuit is closed or open / voltage is high or low. 1 0

  4. Bits and Bytes • A binary digit (1 or 0) is known as a ‘bit’, short for BInarydigiT. • In modern computers bits are grouped in 8 bit bytes. • A Nibbleis 4 bits (half a byte). • A Word is the number of bits that the CPU can process simultaneously. • Determines the speed of the computer. • Processors can have 8-, 16-, 32-(standard) or 64-(fast) bit word sizes (or more).

  5. Character set • The symbols that a computer (software) can recognise which are represented by binary codes that the computer understands.

  6. Character Representation • Over the years different computer designers have used different sets of binary codes for representing characters in a character set. • This has led to great difficulty in transferring information from one computer to another. • i.e. which binary code represents each character

  7. ASCII (American Standard Code for Information Interchange) • Represents each character in a standard character set as a single byte binary code. • The standard code form that most PCs use to allow for communication between systems. • Usually uses a 7 bit binary code so can store 128 different characters and simple communications protocols. • Sufficient for all characters on a standard keyboard plus control codes. • Can be extended (extended ASCII) to use 8 bits (so can store 256 characters) to encode Latin language characters.

  8. ASCII code • The first 32 ASCII codes are used for simple communications protocols, not characters. • e.g. ACK – acknowledge and would be sent by a device to acknowledge receipt of data. • 0110010 – 2 • 0110001 – 1 • ….. • 1000001 – A • 1000010 – B • Note: Letters have increasing values from a-z or A-Z.

  9. Representing Characters and Numbers • e.g. If the ‘A’ key is pressed ‘1000001’ is sent to the CPU. • If the 1 key is pressed then ‘0110001’ is sent to the CPU. • If the user wants to print ‘123’ the codes for 1, 2 & 3 are sent to the printer.

  10. Sorting • Characters are compared in turn from the start of each word (left side) until two characters are different. • The character with the highest ASCII value determines which is the second word. • If 2 words are the same when one ends then the longer word is the second word.

  11. Binary Arithmetic Rules • 0 + 0 = 0 • 0 + 1 = 1 • 1 + 0 = 1 • 1 + 1 = 0 (carry 1) • 1+1+1 = 1 (carry 1)

  12. Arithmetic • ASCII coding is fine for input and output but useless for arithmetic: • 2 0110010 • -1 - 0110001 • 1 0000000 i.e. not 1 • There is no easy way to perform calculations on the numbers stored in this way. • Numbers which are to be used in calculations are therefore held in binary format.

  13. Decimal or Denary system • 134 = 100 + 30 + 4 • Each column is worth 10X as much as the last i.e. base 10 (10 fingers!).

  14. Binary system 134 = 128 + 4 + 2 Each column is worth 2X as much as the last i.e. base 2. Most Significant Bit (MIB) Least Significant Bit (LIB) Increasing Bit Status

  15. Binary – Decimal Spreadsheet Converter 1 • Try using it to ‘play’ with binary numbers. • http://mrleeict.comule.com/as/1%20Programming/1.1%20Data%20Representation/Binary-Decimal%20converter.xls

  16. Denary -> Binary e.g. 117 • Always use the column headings for a byte (8 bits). • 117 < 128 so put a 0 and repeat. 117 > 64 so put a 1. 117 - 64 = 53 , 53 > 32, so put a 1. 53 - 32 = 21 , 21 > 16, so put a 1. Continue this until:

  17. Binary-> Denary e.g. 10110110 Put the column headings above the binary number and add up all the columns with a 1 in them. So 10110110 = 128 + 32 + 16 + 4 + 2 = 182 (denary)

  18. Questions 1. Convert the following binary numbers to decimal. • 0011 • 3 • 0110 • 6 • 1010 • 10 • 01000001 • 65 • 01000101 • 69

  19. 8 bit patterns • Because in modern computers bits are grouped in 8 bit bytes numbers in binary format are usually written in 8 bit patterns even if there are unnecessary left leading 0’s. • e.g. 11(binary) = 3 (decimal) • But you will usually find it written as 00000011

  20. Decimal -> Binary Questions 2. Convert the following decimal numbers to binary: • 5 • 00000101 • 7 • 00000111 • 1 • 00000001 • 26 • 00011010 • 68 • 01000100 • 137 • 10001001

  21. Size of number • Using only one byte to hold a number of places a restriction on the size of number the computer can hold. • Therefore four or more consecutive bytes are commonly used to store numbers

  22. Binary -> Decimal Questions 3. What is the largest decimal number that can be held in (hint: 2^no. of bits): • 1 byte • 255 (2^8 - 1) • 2 bytes • 65535 (2^16 - 1) • 3 bytes • 16777215 (2^24 - 1) • 4 bytes • 4294967295 (2^32-1)

  23. Integers • Integers are whole numbers with which arithmetic can be done. • Stored by the computer as binary numbers using a whole number of bytes. • It is usual to use either 2 bytes (called short integers) or 4 bytes (called long integers), the difference being simply that long integers can store larger numbers.

  24. Boolean Variables • (Yes / No) or (True / False) data • Example uses - a particular bit in memory can be set to show if: • a disk drive is connected or not • the ‘Break’ key is pressed

  25. Plenary • What is meant by an ASCII character?

  26. Plenary • A member of a standard character set. • Set of binary codes the computer understands. • Represented in a single byte/7 or 8 bits used per character. • Standard nature allows for communication between systems.

  27. Plenary • A member of a standard character set. • Set of binary codes the computer understands. • Represented in a single byte/7 or 8 bits used per character. • Standard nature allows for communication between systems.

  28. Plenary • Convert 101 (denary) to binary.

  29. Plenary • 01100101

  30. Plenary • Convert 10011111 to denary.

  31. Plenary • 159

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