Hex and Octal

• There are two bases that we tend to use when working in binary.
• Octal is base 8
• Hexadecimal or hex is base 16.
• We use these as a shortcut for writing binary.
  • Past a few bits numbers in binary are hard to write correctly.
  • There are a bunch of digits
  • And these digits are mostly the same (0,1)
  • Conversion to/from decimal is cumbersome
• Notice that with 3 bits we can represent all of the base 8 digits.
• And with 4 bits we can represent all the base 16 digits

  Binary	Octal	Decimal	Hex
  0000	0	0	0
  0001	1	1	1
  0010	2	2	2
  0011	3	3	3
  0100	4	4	4
  0101	5	5	5
  0110	6	6	6
  0111	7	7	7
  1000	10	8	8
  1001	11	9	9
  1010	12	10	A
  1011	13	11	B
  1100	14	12	C
  1101	15	13	D
  1110	16	14	E
  1111	17	15	F

• Binary/Octal conversions
  • To convert a binary string to octal,
    1. group the digits into sets of three from the right.
    2. Pad the left most group with 0 if needed.
    3. Write the corresponding octal digit for each set.

    • Convert Binary to Octal
      101101011012 = 010 110 101 1012  
                   =  2   6   5   58
                   = 26558

  • Octal string to binary string:
    • Replace the octal digits with the binary representation. Convert Octal to Binary 4623₈ = 4 6 2 3₈ = 100 110 010 011₂ = 100110010011₂
• Hex/Binary conversions
  • Use the same procedure.
  • But groups of 4.
  • You should memorize A=10, B=11, C=12, D=13, E=14, F=15
  • Or come up with a quick way to figure it out (like a quick table)

  • Binary to Hex
    1011011111111012 = 0101 1011 1111 11012
                     =   6   B    F    C16
                     = 6BFC16
    Hex to Binary
    C4AD16 =   C    4    A    D16
           = 1100 0100 1010 11012
           = 11000100101011012