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 <Previous Next>
