                                  T H E

                               Z E P H Y R

                      __     M A G A Z I N E
                     {__]++++++++++++++++++++++++++[]
                     Issue #67                8-04-89

                A weekly electronic magazine for users of
                            THE ZEPHYR II BBS
                        (Mesa, AZ - 602-894-6526)
                    owned and operated by T. H. Smith

                        Editor - Gene B. Williams

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                                (c) 1989

         The "equality issue" is complete, but I thought it more
    appropriate to give space to another guest contributor, namely
    Michael Setzer. (Look at the list of back issues. The vast
    majority are mine - so it's kinda nice to have some "new blood"
    on the board.)
         Two reminders:
         One - Michael Setzer is author of this week's issue, not me.
    Credit, questions and comments should all go to him.
         Two - I'm always open to guest issues. If you'd care to
    contribute, contact me in E-mail. Better yet, start by down
    loading issue #27 (ISH.27). That will give you all the
    information you need. If you have any other questions, then
    contact me.

                The Secrets of Converting Hex to Decimal

                  By Andrew Bartels and Michael Setzer

         Before getting into how to convert between the different
    numbering systems, it is necessary to understand what a numbering
    system is and how it is organized.  Take for instance decimal, a
    very familiar numbering system.  It is called this because its
    base is ten.  That is, everything written in decimal can be
    expressed as a power of 10.  For example, when when the number
    2304 is written, it can be written like this when more expressive
    math is used.

        (2*1000)+(3*100)+(0*10)+(4*1)

                      OR,

               3       2       1       0
              2*10  + 3*10    0*10    4*10

    (Those numbers along the top are exponents)

         Thus the entire number (which is the number of bytes in a
    granule), is represented in terms of powers of ten, with each
    digit (from right to left) progressively being worth one more
    power of ten.
         Now for a look at hexadecimal.  It is called this because it
    is a numbering system based on 16.  All hex numbers can be
    written in terms of powers of 16.  In decimal (our first
    numbering system), we have the digits 0-9.  Each place in the
    decimal number (that is like the tens place, hundred place, Etc)
    must iterate from 0-9 before the next place iterates.  Ex:  you
    must iterate from 0 to 9 before the ones colum is returned to
    zero and the tens column becomes 1.
         Hexidecimal has the following possible digits: 0-9, and
    A,B,C,D,E,F.  Thus there are 16  possible digits for each column.
    Note here that the hex digit "A" comes after 9, and that once a
    hex column iterates from 0 to f, it is returned to 0, and the
    next column over, it is incremented by one. This is the same
    procedure that is used used when working with the decimal system.
    With Decimal however, there are only 10 positions to work with.

         Now for a little comparasion as to see the relationship of hex to
    decimal.  Observe the following table:

           HEX DIGIT   DECIMAL NUMBER
    --------------------------------------------
              0               0
              1               1
              2               2
              .               .
              .               .
              .               .
              9               9
              A               10
              B               11
              C               12
              D               13
              E               14
              F               15
    -------------------------------------------

         It can now be seen that a Hex digit "A" literally equates to
    10 in decimal, "B" corresponds with decimal 11, and so forth.
    What would hex "10" translate to decimal?  Hex numbers range from
    "0" to "F" before the next column is incremented.  Therefore,
    "10" hex  is 16 in decimal. (that is, F+1=10.)

         Suppose you have the hex number 1234.  It can be written as:

              3       2       1       0
          1*16  + 2*16  + 3*16  + 4*16

         It is the same pattern with decimal, but if the numbers are
    tallied, it can be seen that the number is actually 4660 in
    decimal.

         Now we will attempt to convert a Hex number with the digits
    "A" to "F" in it.  As was previously discussed, the numbers above
    9 inhexidecimal are represented this way:    A=10, B=11, C=12,
    D=13, E=14, F=15, and so forth.  Simply substitute the digit "A"
    to "f" with its decimal equivalent when calculating.  Try
    converting Hex 8C1B to its decimal equivalent.

             3        2       1        0

            8*16  + 12*16  + 1*16  + 11*16

         Notice that the HEX DIGIT "C" has been changed to its
    decimal equivalent, 12, andd that the hex "B" is now decimal 11.
    This type of conversion is necessary in order to express the hex
    numberr in entirely decimal terms.  Observe the following:

             3                  2
            8*16 = 32768 AND  12*16 = 3072

             1                  0
            1*16 =    16 AND  11*16 = 11
          ------              ------
          32784   plus this   3083

    equals 35867.  Therefore,  Hex "8C1B" equals decimal 35867!. It
    is that simple.  Simply convert HEX numbers to decimal by using
    the powers of 16...

    Until Next Time

         Okay, does everyone get that?
         This might be a good issue to download, print out and keep
    around for reference.

         Also on hold is an update of Chris Mitchell's article on how
    to get into radio broadcasting. I might go ahead and put that one
    up next week, or it might be delayed one more week (or so) for
    the long-promised issue.
         Other than that, what comes next depends on a number of
    factors. Personally, I'd love to see more contributions from the
    users, with my own writing going up only to fill the gaps. In
    fact, I'd kinda like to have more contributions than there is
    room to run.
         Dream on, Gene. Dream on.

Zephyr Magazine is © Gene Williams. All rights reserved.