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How to convert an exponent to binary number?

  1. Jun 13, 2003 #1
    how to convert an exponent to binary number?
     
    Last edited by a moderator: Feb 5, 2013
  2. jcsd
  3. Jun 13, 2003 #2

    chroot

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    What you say does not make much sense -- you can convert any number into any base you want.

    Please provide an example of what you're trying to do so that we can help you better.

    - Warren
     
  4. Jun 13, 2003 #3
    i read the next statement at this webpage:http://www.mersenne.org/math.htm
    "Convert the exponent 23 to binary, you get 10111."
     
  5. Jun 13, 2003 #4
    That's not an exponent, just a number in binary form. To convert we do the following

    16 8 4 2 1
    1 0 1 1 1

    So, we have one 16, no 8, one 4, one 2, and one 1. We sum them to get 16+4+2+1=23. The division algorithm can be used to convert from decimal to binary.

    23-16=7, so we put a 1 in the 16 column.
    7-8<0, so we put a 0 in the 8 column.
    7-4=3. so we put a 1 in the 4 column.
    3-2=1, so we put a 1 in the 2 column.
    2-1=1, so we put a 1 in the 1 column.

    Thus, 23 in binary form is 10111.
     
  6. Jun 13, 2003 #5

    HallsofIvy

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    The thing that was confusing was that you were asking about
    "converting an exponent". You are really just asking about converting a number. The fact that the number happens to be an exponent in the formula is not important.

    Another way to do the same thing is:

    2 divides into 23 11 times with remainder 1
    2 divides into 11 5 times with remainder 1
    2 divides into 5 2 times with remainder 1
    2 divides into 2 1 time with remainder 0
    2 divides into 1 0 times with remainder 1

    Now that we have reached "0 times" write the remainders in reverse order : 10111 base 2 is 23 base 10.
     
  7. Jun 13, 2003 #6

    Integral

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    HallsofIvys methods works for conversion from base 10 to any base, simply divide by the base, the remainder gives the digits in the new base, starting with the least significant.
     
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