Data Representation & Boolean Algebra

Convert the following:

     i) (127.6)₈ = (?)₁₆
     ii) (AFED.15)₁₆ = (?)₁₀

• To convert base-8 to base-16, firstly we will convert base-8 to base-2 and then to the base-16 we know, every no. has its own binary notation.
• Here,
  STEP1: 127 can be written as : 001 010 111
  STEP2: Group these into the groups of four starting with extreme right.
  STEP3: It will appear as : 0 0101 0111
  STEP4: As the leftmost bit is not complete, put the zeros to balance it.
  STEP5: Now considering the conversion table : the base-16 value comes out to be 57

• We will do this conversion in steps.
  
  STEP 1: We know the pattern 0 1 2 3 4 5 6 7 8 9 A B C D E F.
  now, the digits that are given to us are to be compared with this for their positions.
  STEP 2: The positions are as follows:
  A = 10
  F = 15
  E = 14
  D = 13
  STEP 3: Starting from the extreme right multiply each digit with 16 raised to the power starting with 0.
  STEP 4: The expression that we got is:
  10*(16^4) + 15*(16^3) + 14*(16^2) + 13*(16^1) + 15*(16^0)
  STEP 5: Solving the above fraction, we get 720607
  STEP 6: The base 10 value is thus 720607