Codes

• Code


  A symbolic way to represent information. In qualitative inquiry, a code is most often a word or short phrase symbolically assigned as summative, salient, essence-language-based or visual data
• Decimal System


  Conventional number system with 10 symbols: 0,1,2,3,4,5,6,7,8,9
• Positional Notation


  • Positions of the digits indicate the place value. Each place value is of the power of 10
  • For 3,40510 is a decimal number: 3 - thousands digit (3 x 103), 4 - hundreds digit (4 x 102), 0 - tens digit (0 x 101), 5 - units digit (5 x 100)
• Binary Code


  A base-2 number system representing numbers using a pattern of ones and zeroes. Early computer systems had mechanical switches that turned on to represent 1, and turned off to represent 0. A digital one or zero is simply an electrical signal that's either turned on or turned off inside of a hardware device. Binary numbers consist of a series of eight "bits," which are known as a "byte". A bit is a single one or zero that makes up the 8 bit binary number.

  
• Positional Notation (Binary)


  • Positions of the digits indicate the place value. Each place value is of the power of 2
  • For 10102 is a binary number: 1 - (1 x 23) = 8, 0 - (0 x 22) = 0, 1 - (0 x 21) = 2, 0 - (0 x 20) = 0, = 8 + 0 + 2 + 0 = 1010 is the decimal number

  
• Converting Decimal to Binary and vice versa

  1. Binary to decimal: 1 0 0 12 = 1(23) + 0(22) + 0(21) + 1(20) = 8 + 0 + 0 + 1 = 910

  2. Decimal to binary: 2510 = 25/2 = 12 r. 1, 12/2 = 6 r. 0, 6/2 = 3 r. 0, 3/2 = 1 r. 1, 1/2 = 0 r. 1 = 110012

  
• Bit


  The smallest unit of storage, storing only 1 or 0
• Byte


  Groups of 8 bits
• There are 256 possible outcomes for 1 byte, ranging from 0 to 255 or -128 to 127
• Signed integers


  Represent positive and negative numbers. For 1 byte, the range is -128 to 127

  
• Unsigned integers


  Represent only positive numbers. For 1 byte, the range is 0 to 255

  
• Boolean Logic


  A branch of algebra that will lead to exactly two results (true or false)
• Boolean Operators


  • And - used to confirm that two or more Boolean expressions are all true
  • Or - checks that either one condition or another is true
  • Not - only takes one argument and negates it
• Computer Addition


  1. 0 + 0 = 0

  2. 0 + 1 = 1

  3. 1 + 1 = 10
• Computer Addition Examples


  • 110012 + 101112 = 1100002
  • 11012 + 10112 = 1100012
  • 2410 + 510 = 110001012
  • 10002 + 100010 = 110001012
• Text data


  Texts and symbols presented in computer screen are transmitted in binary codes, which are converted into texts and symbols by means of standard American Standard Code for Information Interchange (ASCII) code

  
• Text data examples


  • Apple = 01000001 01110000 01110000 01101100 01100101
  • Hello, World! = 01001000 01100101 01101100 01101100 01101111 00101100 00100000 01010111 01101111 01110010 01101100 01100100 00100001
• Hexadecimal Number System


  A number system with a base of 16, using symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

  
• Octal Number System


  A number system with a base of 8, using symbols 0, 1, 2, 3, 4, 5, 6, 7
• Conversion


  1. Binary to hexadecimal: 100010102 = 8A16

  2. Hexadecimal to binary: 2516 = 00100101

  3. Binary to octal: 100010102 = 2128

  4. Octal to binary: 178 = 11112

  
• Hexadecimal to ASCII conversion

  • 49 66 20 77 65 20 68 61 76 65 20 61 20 71 75 69 7A 2C 20 65 76 65 72 79 62 6F 64 79 20 69 73 20 72 65 71 75 69 72 65 64 20 74 6F 20 62 72 69 6E 67 20 74 68 65 20 41 53 43 49 49 20 74 61 62 6C 65 2E 20 49 74 20 69 73 20 72 65 71 75 69 72 65 64 2E
• Octal to ASCII conversion

  • 124 150 145 040 101 123 103 111 111 040 164 141 142 154 145 163 040 141 162 145 040 141 154 162 145 141 144 171 040 160 162 157 166 151 144 145 144 040 142 171 040 164 150 145 040 151 156 164 145 162 156 145 164 040 141 156 144 040 142 171 040 164 150 151 163 040 160 162 145 163 145 156 164 141 164 151 157 156 056
• Error


  Any flaw or deviation that occurs while the information is transmitted from the source to the destination in a computer network
• Error Correction


  The method of replacing the deviated bits sequence with the right bit sequence so that the receiver can accept the data and process it
• Types of Error


  • Single Bit Error - Only one bit of the frame received is corrupt
  • Multiple Bit Error - More than one bit received in the frame is found to be corrupted
  • Burst Error - More than one consecutive bit is corrupted in the received frame

  
• Types of Error Correction

  • Forward Error Correction - The receiving end is responsible for correcting the network error, no need for retransmission
  • Backward Error Correction - The receiver needs to correct the error either by transmitting the corrupted message or retransmitting the entire message
  • Hamming Code Error Correction - Extra parity bits are appended to the message which are used by the receiver to correct single bit and multiple bit errors

  
• Error Detecting Codes


  Codes used to detect the errors present in the received data bitstream, containing some bits appended to the original bit stream to detect errors during transmission

  
• Parity Code


  Even Parity Code - The value of even parity bit should be zero if even number of ones present, otherwise one

  Odd Parity Code - The value of odd parity bit should be zero if odd number of ones present, otherwise one
• Even Parity Code


  If the other system receives one of these even parity codes, then there is no error in the received data. If the other system receives other than even parity codes, then there will be errors in the received data and we can't predict the original binary code.

  
• Odd Parity Code


  If the other system receives one of these odd parity codes, then there is no error in the received data. If the other system receives other than odd parity codes, then there is an error in the received data and we can't predict the original binary code.
• Parity bit is only useful for single bit error as a multiple bit error presents a difficulty in determining the original number of bits
• Hamming Code


  Error correction code that appends parity bits to the original data to detect and correct single-bit errors

  
• Hamming Code Example


  For a 4 bit system, the hamming code would be b7 b6 b5 b4 b3 b2 b1

  The position of the parity bits will be located at b1, b2 and b4 (powers of 2: 20, 21 and 22)

  Example: For the binary 100, the hamming code is 10010112 where the parity bits are added to make the number of 1s even in each parity group

  
• Hamming Code Examples


  • 111012 = 10010112

  258 = 100000102

  10002 to base 7 = 208

  1002 to base 5 = 202