Converting / Data Storage

• bits to bytes


  divide by 8
• Data needs to be converted into a binary format to be processed by a computer
• Hexadecimal to Denary

  Multiply each character together

  e.g. 87 hexadecimal to denary

  256 16 1

  8 7

  multiply numbers in a column

  16 x 8 = 128

  1 x 7 = 7

  add the numbers together

  128 + 7 = 135

  hexadecimal number 87 is 135 in denary
• Denary to Hexadecimal 


  divide and use remainders

  e.g. denary number 106 to hexadecimal

  divide 106 by 16 = 6 (remainder 10)

  divide the remainder (10) by 1 = 10 = A in hexadecimal

  denary 106 = 6A hexadecimal
• Binary to Hexadecimal (split into nibbles)

  each hexadecimal character is equal to a nibble in binary

  split the binary code into 4-bits to convert binary to hex

  e.g. binary 10111001

  split into 1011 1001

  Draw a table

  8 4 2 1 8 4 2 1

  1 0 1 1 1 0 0 1

  add up the top values if they have a 1 in the column below

  8+2+1 = 11 = B

  8+1=9

  binary number 10111001 is B9 in hexadecimal
• Hexadecimal to Binary

  first convert to denary

  e.g. 8C to binary

  in denary: 8 = 8, C = 12

  Find binary value using table

  8 4 2 1 8 4 2 1

  1 0 0 0 1 1 0 0

  in binary: 8 = 1000, C = 1100

  hexadecimal 8C is 10001100 in binary
• Add Binary number togethers

  Add 10001101 and 01001000

  Put the binary number into columns(/tables)

  from the right add the numbers

  1 0 0 0 1 1 0 1

  0 1 0 0 1 0 0 0

  1 1 0 1 0 1 0 1

  binary answer = 11010101
• Overflow Error


  Happens during binary arithmetic when the result is more bits than the CPU is expecting

  Computer stores extra bits elsewhere to deal with it

  When doing binary addition and the answer is 9-bit, ignore the overflow and give an 8 bit answer
• Binary Shift

  used to multiply and divide by 2
• Left Shift

  Multiply

  for every place shifted left, number is doubled
• Right Shift


  Divides

  for every place shifted right, number is halved