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Have you ever started a relatively simple investigation into a trivial matter,
only to find yourself going down the metaphorical "rabbit
hole" even after finding the original answer? Such was the case for me when
someone sent me an email with a signature that included his amateur radio call
sign. The first three characters, KB3, matched mine and that got me wondering on
what date his call sign was granted compared to mine.
Let us say for example* the writer's call sign was KB3PGM and mine is (actually)
KB3UON. I looked them up in the FCC's
Universal Licensing System (ULS) selfserve license search database
and discovered KB3PGM was granted on May 31, 2007. Mine, KB3UON, was granted on
May 24, 2010  almost exactly three years apart. My next thought was to wonder how
linearly new call signs are assigned; that is, would choosing a date exactly in
the middle of our two turn up a call sign that was granted also exactly (or nearly
so) in the middle of our two?
Calculating the middle date is easy enough by finding the average of his and
mine in Excel. That result is November 25, 2008. Determining the call sign exactly
in the middle was a little more work, since Excel will not calculate the series
of characters numerically in the middle of two character strings. I needed a fairly
simple way to find that middle call sign of KB3_ _ _.
Having recently read an article on the various number system bases of civilizations
throughout history, it occurred to me that the scientific way to determine the center
value would be to convert the threecharacter strings from a base26 system (the
English alphabet) to our familiar base10 system, calculate the mean, then convert
back to base26 and find the equivalent characters. Excel was used to do the calculations,
even though it does not have a builtin function. Here is how I did it.
Grant Date 
May 31, 2007 
May 24, 2010 
Character Positions (last 3) 
16(P) 7(G) 13(M) 
21(U) 15(O) 14(N) 
Base10 Conversion 
16×26^{2} + 7×26^{1} + 13×26^{0}
10816 + 181 + 13 = 11011

21×26^{2} + 15×26^{1} + 14×26^{0}
14196 + 390 + 14 = 14600

The mean (middle) value call sign (base10) = (11011 + 14600) / 2 = 12805.5 >>
12805
Character positions (last 3) are:
INT(12805/26^{2}) = 18, r=637 >> char(18) = R
INT(637/26^{1}) = 24, r=13 >> char(24) = X
INT(13/26^{0}) = 13, r=0 >> char(13) = M
The middle call sign, then, is KB3RXM.
The ULS shows its grant date is November 17, 2008. That is within eight days
of the chronological middle date of November 25, 2008, or 8 parts in 1089 (0.73%).
The results supports the claim that call signs are assigned in a linear manner as
requested and that the rate of granting is approximately evenly distributed. I ignored
the few unallowed character combinations and vanity call signs.
What's my point, you may be asking? There really is no point other than satisfying
myself that call signs are probably granted in a sequential manner as the FCC claims,
with the surprising result that at least for the two dates tested, amateur radio
licenses are being earned at an approximately even (linear) rate. The other nonpoint
is demonstrating my method for attacking the inquiry mathematically rather than
counting on my fingers and toes to determine the middle call sign letters. I could
explore further by testing points inbetween to see whether grant dates are evenly
distributed or clustered in a way that caused the mean to fall in the middle, but
there's point in it.
* Please do not contact the licensees used in this example. I had to choose active
call signs for the example.
Posted February 14, 2018
