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posted by  TayTayOSU on 11/6/2009 5:08:57 PM  |  status: Closed  |  Earned Karma: 68

Discrete Math!

Course Textbook Chapter Problem Needs by
Discrete Math Discrete Math and Its Applications (6th) by Rosen N/A N/A 11/8/2009 at 11:59:00 PM
Question Details:
Convert binary numeral to 
(a) decimal notation
(b) base 3 notation
(c) octal notation
(d) hexadecimal notation

Binary Numeral:
1010 1010 1010



Please show steps to all 4 clear for lifesaver points! Thanks! 
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posted by leettab on 11/7/2009 5:31:29 PM  |  status: Live
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Response Details:
First I will convert the binary number to decimal (base 10)

If we look at the right most position in the binary number its place value is .  The next position immediately to the
left is and so on as we move from right to left.


we will thus have




this becomes


So our decimal number is


Now onto base 3.  Start off by dividing 2730 by 3.  Keep track of remainders.  If there are none then the
place value will be zero.  Keep dividing until you get to where 3 won't go but only zero times.  The
number is built from the remainders from right to left

   remainder 0

     remainder 1

     remainder 0

       remainder 2

         remainder 0

           remainder 2

             remainder 0

             remainder 1


So the base3 number is

we can check this by applying the same logic we use with the binary number.






Now we can apply the same algorithm to find base 8 (octal)


  remainder 2

      remainder 5

          remainder 2

            remainder 5

So the base 8 number is

we can check this using the same logic we did for the other 2






Now for base 16  (hexadecimal)


  remainder 10

      remainder 10

         remainder 10

Now remember that for hexadecimal, 10 thru 15 are represented by A B C D E F

so our hexadecimal number is

we can check this as the others
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