[an error occurred while processing this directive] ZEPHYR Magazine
                              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.   



           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:

          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 
     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.