computer

• Binary arithmetic check card


  • Binary headings (128, 64, 32, 16, 8, 4, 2, 1)
  • 1 + 1 = 0 carry 1; 1 + 1 + 1 = 1 carry 1, etc.
  • Two's complement uses −128 in left-most bit position
  • Shifting binary numbers left is the same as multiplying by factors of 2
  • Shifting binary numbers right is the same as dividing by factors of 2
• The binary number system is chosen because it consists of 1s and 0s only which correspond to ON and OFF states in the computer system
• Binary number system


  Based on the number 2, can only use the two values 0 and 1 (bits)
• Denary number system


  Base 10 number system
• Converting from hexadecimal to binary

  Write the 4-bit binary code for each hexadecimal digit
• Converting from hexadecimal to denary


  Multiply each hexadecimal digit by its heading value and add them together
• Converting from denary to hexadecimal

  Carry out successive divisions by 16 until zero value results, read the remainders from bottom to top
• Uses of the hexadecimal system


  • Error codes
  • MAC addresses
  • IP addresses
  • HTML colour codes
• Binary addition


  Involves a carry and a sum for each of the 2 or 3 bits being added
• Overflow occurs if the result of a calculation is too large for the allocated word size
• Logical binary shifts


  Shifting (moving) bits to the left (multiplying by 2 for each shift) or the right (dividing by 2 for each shift)
• Two's complement


  Allows for the representation of negative integers
• The right-most bit in two's complement represents -128
• Converting denary numbers into binary in two's complement format

  Place 1-bits in the appropriate position remembering that the right-most bit now represents −128
• Two's complement notation


  Allows for the possibility of representing negative integers
• Converting negative denary numbers into binary in two's complement format


  One method: Put 1-bits in their correct places

  Another method: Write the positive binary value, invert each bit, then add 1
• The binary representation of −67 in two's complement format is 10111101
• Shifting a binary number left by two places is equivalent to multiplying by 22 = 4
• Shifting a binary number right by two places is equivalent to dividing by 22 = 4
• Adding 220 (in binary) to 44 (in binary) results in an overflow error as the sum exceeds the maximum 8-bit value of 255
• To convert a positive denary number to two's complement binary, invert the bits and add 1
• Lossy file compression


  File compression algorithms eliminate all unnecessary data and the original file can no longer be reconstructed; some data is irretrievably lost
• Lossless file compression


  Data from the original uncompressed file can be reconstructed following application of the lossless compression algorithms; no data is lost
• Examples of lossy and lossless compression

  • Lossy: MPEG, JPEG
  • Lossless: Run Length Encoding (RLE)
• Data skewing


  Bits arrive at their destination no longer synchronised
• USB-C connection


  The latest type of USB connector, which uses a totally symmetrical 24-pin USB connection, so it will fit into a USB port either way round since there is no up or down orientation
• Parallel data transmission


  Data is being sent 8 bits at a time down eight wires in one direction only
• Half-duplex data transmission


  Data is being sent in both directions, one bit at a time along a single wire, but not at the same time
• Data is being sent 16 bits at a time along 16 individual channels in both directions simultaneously
• Data is being sent one bit at a time down a single wire; the transmission occurs in both directions simultaneously
• Errors can occur during data transmission due to electrical interference, packet switching, and skewing of data
• Parity check


  A method used to check whether data has been changed or corrupted following data transmission
• Checksum


  A method used to check if data has been changed/corrupted following data transmission
• Echo check


  Requires data to be sent back to the sending computer where it is compared with the data originally sent
• Echo check is not a very reliable method for detecting errors as it is unclear where the error occurred
• Check digits


  Used to identify any errors following data entry
• Automatic Repeat Request (ARQ)


  A way to check data following data transmission, often used by mobile phone networks to guarantee data integrity
• ARQ uses positive and negative acknowledgements and timeout to detect and correct errors
• When data is transmitted over public networks, there is always the risk of it being intercepted. Using encryption and encryption keys helps solve this problem or certainly makes it more difficult for the hacker
• Encryption alters the data into a form that is unreadable by anybody for whom the data is not intended