Computer Science

• Data RepresentationNumber SystemsBinary System

  • Base 2 number system
  • It has two possible values only (0 and 1)
  • 0 represents OFF, and 1 represents ON
  • A point to be noted is that the most left bit is called the MSB (Most Significant Bit)

  Denary System

  • Base 10 number system
  • Has values from 0 to 9

  Hexadecimal (aka Hex)

  • Base 16 number system
  • Have values from 0 to 9 followed by A to F
  • A represents 10, B represents 11 and so on until 15, which is F
• Binary Value-Hexadecimal Value-Denary Value

  0000-0-0

  0001-1-1

  0010-2-2

  0011-3-3

  0100-4-4

  0101-5-5

  0110-6-6

  0111-7-7

  1000-8-8

  1001-9-9

  1010-A-10

  1011-B-11

  1100-C-12

  1101-D-13

  1110-E-14

  1111-F-15
• Number ConversionsConverting Binary to Denary

  • Place the binary value in columns of 2 raised to the power of the number of values from the right starting from 0. e.g. For binary value 11101110, place it in a table like this:
  • 128- 64- 32- 16- 8- 4- 2- 1
  • 01- 01- 01- 01- 01- 01- 01- 01
  • As can be seen it starts from 1 and then goes to 128 from left to right
  • Now values with 1 are to be added together, giving the final answer, as for the example, it is 128 + 64 + 32 + 8 + 4 + 2 = 238