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Various reverse-engineered versions of the allocation algorithmsused by different countries to allocate 24-bit ICAO addresses based
on the aircraft registration These were worked out by looking at the allocation patterns and working backwards to an algorithm that generates that pattern,spot-checking aircraft to see if it worked.
YMMV.

    registration_from_hexid = (function () {

    // hide the guts in a closure



    var limited_alphabet = "ABCDEFGHJKLMNPQRSTUVWXYZ"; // 24 chars; no I,O

    var full_alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";  // 26 chars







  // handles 3-letter suffixes assigned with a regular pattern

  //

  // start: first hexid of range

  // s1: major stride (interval between different first letters)

  // s2: minor stride (interval between different second letters)

  // prefix: the registration prefix

  //

  // optionally:

  //   alphabet: the alphabet to use (defaults full_alphabet)

  //   first: the suffix to use at the start of the range (default: AAA)

  //   last: the last valid suffix in the range (default: ZZZ)



     var stride_mappings = [

     { start: 0x008011, s1: 26*26, s2: 26, prefix: "ZS-" },



     { start: 0x390000, s1: 1024, s2:  32, prefix: "F-G" },

     { start: 0x398000, s1: 1024, s2:  32, prefix: "F-H" },



     { start: 0x3C4421, s1: 1024,  s2: 32, prefix: "D-A", first: 

     'AAA', last: 'OZZ' },

     { start: 0x3C0001, s1: 26*26, s2: 26, prefix: "D-A", first: 

     'PAA', last: 'ZZZ' },

     { start: 0x3C8421, s1: 1024,  s2: 32, prefix: "D-B", first: 

     'AAA', last: 'OZZ' },

     { start: 0x3C2001, s1: 26*26, s2: 26, prefix: "D-B", first: 

    'PAA', last: 'ZZZ' },

    { start: 0x3CC000, s1: 26*26, s2: 26, prefix: "D-C" },





{ start: 0x3D04A8, s1: 26*26, s2: 26, prefix: "D-E" },





 { start: 0x3D4950, s1: 26*26, s2: 26, prefix: "D-F" },

        { start: 0x3D8DF8, s1: 26*26, s2: 26, prefix: "D-G" },

        { start: 0x3DD2A0, s1: 26*26, s2: 26, prefix: "D-H" },

        { start: 0x3E1748, s1: 26*26, s2: 26, prefix: "D-I" },



        { start: 0x448421, s1: 1024,  s2: 32, prefix: "OO-" },

        { start: 0x458421, s1: 1024,  s2: 32, prefix: "OY-" },

        { start: 0x460000, s1: 26*26, s2: 26, prefix: "OH-" },

        { start: 0x468421, s1: 1024,  s2: 32, prefix: "SX-" },

        { start: 0x490421, s1: 1024,  s2: 32, prefix: "CS-" },

        { start: 0x4A0421, s1: 1024,  s2: 32, prefix: "YR-" },

        { start: 0x4B8421, s1: 1024,  s2: 32, prefix: "TC-" },

        { start: 0x740421, s1: 1024,  s2: 32, prefix: "JY-" },

        { start: 0x760421, s1: 1024,  s2: 32, prefix: "AP-" },

        { start: 0x768421, s1: 1024,  s2: 32, prefix: "9V-" },

        { start: 0x778421, s1: 1024,  s2: 32, prefix: "YK-" },

        { start: 0x7C0000, s1: 1296,  s2: 36, prefix: "VH-" },

        { start: 0xC00001, s1: 26*26, s2: 26, prefix: "C-F" },

        { start: 0xC044A9, s1: 26*26, s2: 26, prefix: "C-G" },

        { start: 0xE01041, s1: 4096,  s2: 64, prefix: "LV-" }

        ];

        function lookup(hexid) {

        var hexid = +("0x" + hexid);



        reg = n_reg(hexid);

        if (reg)

        return reg;



        reg = ja_reg(hexid);

        if (reg)

        return reg;



        reg = hl_reg(hexid);

        if (reg)

        return reg;



        reg = numeric_reg(hexid);

        if (reg)

        return reg;



        reg = stride_reg(hexid);

        if (reg)

        return reg;



        return null;

        }



         function stride_reg(hexid) {

         // try the mappings in stride_mappings

         var i;

         for (i = 0; i < stride_mappings.length; ++i) {

         var mapping = stride_mappings[i];

         if (hexid < mapping.start || hexid > mapping.end)

         continue;



         var offset = hexid - mapping.start + mapping.offset;



         var i1 = Math.floor(offset / mapping.s1);

         offset = offset % mapping.s1;

         var i2 = Math.floor(offset / mapping.s2);

         offset = offset % mapping.s2;

         var i3 = offset;



         if (i1 < 0 || i1 >= mapping.alphabet.length ||

         i2 < 0 || i2 >= mapping.alphabet.length ||

         i3 < 0 || i3 >= mapping.alphabet.length)

         continue;



         return mapping.prefix + mapping.alphabet.charAt(i1) + 

         mapping.alphabet.charAt(i2) + mapping.alphabet.charAt(i3);

         }



        // nothing

        return null;

        }





        // US N-numbers

        //



        function n_letters(rem) {

        if (rem == 0)

        return "";



        --rem;

        return limited_alphabet.charAt(Math.floor(rem / 25)) + 

        n_letter(rem % 25);

        }



        function n_letter(rem) {

        if (rem == 0)

        return "";



       --rem;

      return limited_alphabet.charAt(rem);





      function n_reg(hexid) {

      var offset = hexid - 0xA00001;

      if (offset < 0 || offset >= 915399) {

      return null;

      }



     var digit1 = Math.floor(offset / 101711) + 1;

     var reg = "N" + digit1;

     offset = offset % 101711;

     if (offset <= 600) {

     // Na, NaA .. NaZ, NaAA .. NaZZ

     return reg + n_letters(offset);

     }



     // Na0* .. Na9*

     offset -= 601;



     var digit2 = Math.floor(offset / 10111);

     reg += digit2;

     offset = offset % 10111;



     if (offset <= 600) {

     // Nab, NabA..NabZ, NabAA..NabZZ

     return reg + n_letters(offset);

     }



     // Nab0* .. Nab9*

     offset -= 601;



     var digit3 = Math.floor(offset / 951);

     reg += digit3;

     offset = offset % 951;



     if (offset <= 600) {

     // Nabc, NabcA .. NabcZ, NabcAA .. NabcZZ

     return reg + n_letters(offset);

     }



                // Nabc0* .. Nabc9*

                offset -= 601;



                var digit4 = Math.floor(offset / 35);

                reg += digit4.toFixed(0);

      offset = offset % 35;



      if (offset <= 24) {

      // Nabcd, NabcdA .. NabcdZ

      return reg + n_letter(offset);

      }



      // Nabcd0 .. Nabcd9

      offset -= 25;

      return reg + offset.toFixed



      (0);

The mode s hex code is used in aerospace/navigation.

From wikipedia :

Mode S equipped aircraft are assigned a unique ICAO 24-bit address or (informally) Mode-S "hex code" upon national registration and this address becomes a part of the aircraft's Certificate of Registration. Normally, the address is never changed, however, the transponders are reprogrammable and, occasionally, are moved from one aircraft to another (presumably for operational or cost purposes), either by maintenance or by changing the appropriate entry in the aircraft's Flight management system.

There are 16,777,214 (224-2) unique ICAO 24-bit addresses (hex codes) available.[4][5] The ICAO 24-bit address can be represented in three digital formats: hexadecimal, octal, and binary. These addresses are used to provide a unique identity normally allocated to an individual aircraft or registration.

You can find the aircraft just be googling each mode s hex code, e.g. for the first one: https://www.radarbox24.com/data/mode-s/A00001#1068536488.

The N-code is the Aircraft Registration code. Again, from Wikipedia:

In the United States, the registration number is commonly referred to as an "N" number, because all aircraft registered there have a number starting with the letter N. An alphanumeric system is used because of the large numbers of aircraft registered in the United States. An N-number begins with a run of one or more numeric digits, may end with one or two alphabetic letters, may only consist of one to five characters in total, and must start with a digit other than zero.

I do not think there is any mathematical or logical relationship between the mode s hex and the aircraft registration code !!