Convert octal to hex, w/out converting to Binary

  1. I have been trying to convert a from octal to hex and hex to octal without using binary. I believe the method is called repeated divison.

    Example of problem I am trying to solve,

    Convert 173 octal(123 dec) to hex


    173 oct / 16 oct = 10 oct remainder 13 oct

    10 oct / 16 oct = 0 oct remainder 10 oct


    Reading up (1st division remainder is less sig. digit, and last is most sig.)


    answer 1013 hex = 4115 dec. WRONG

    answer should be 7B Hex
     
  2. jcsd
  3. ehild

    ehild 12,361
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    You can not mix octal and decimal numbers, and that "16" was decimal. Apply the repeated division on the decimal form of octal 173:

    123=7*16 +11 which is 7B in hexadecimal form.

    The conversion is possible also without using decimal form.
    Working in the "hexadecimal word" 8=10/2

    173 (oct) = 3+7*8+1*8*8 =3+7*10/2+1*10/2*10/2=
    =3+(6*10/2+10/2) + 10/2*8=
    =3+(3*10+8)+(4*10)=(3+4)*10+(3+8)=7*10 + B = 7B

    (It is similar backwards. You know that the base of the hexadecimal numbers is 20 in your octal system. If you have 173(hex), for example, it is
    3+7*20+1*20^2=3+(7*2)*10+4*100=
    3+(10+6)*10+4*100=3+6*10+5*100=563.)

    ehild
     
  4. You can get this to work if you 1) Use the correct representation of the hexadecimal base (20 oct) and 2) Interpret remainders as single hexadecimal digits (which they must be).

    173 oct / 20 oct = 7 oct remainder 13 oct (B hex)

    7 oct / 20 oct = 0 oct remainder 7

    Reading up (1st division remainder is less sig. digit, and last is most sig.)
    answer 7B hex
     
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