There is no great mystery or difficulty involved in determining by computer whether a serial number is affected by an AD.  First it is important to note that the serial number itself is not searched, only that portion of the number that represents the manufacturing sequence.  More about this later.   The search methodology involves establishing ranges of applicability and then having the computer check the ranges to see if the target number is included.   Every AD can be described as a number of ranges.  All that's really needed is to read each of the 5,000 plus ADs, decide if there are serial numbers in them and then type them into a database.  Of course, reading 5,000 ADs and a few thousand more service bulletins, some with thousands of serial numbers, critically, and then typing about 40,000 serial number ranges accurately takes pretty stout buns and pretty thick eye glasses.  The search program used by ADR took 3 years to develop and 2 more years to test.

Example 1:  An AD applies to a certain airframe S/Ns 523 thru 599 and 604 thru 615.  The database coding is set in ranges, like this:

From	Thru
523	599
604	615

Example 2:  An AD applies to airframe S/Ns 118 thru 612 except for 178, 212, and 415.  The database coding would be set as follows:

From	Thru
118	177
179	211
213	414
416	612

Now back to serial number and manufacturing sequence numbers (MSN).  Serial number often contain a great deal more information that just the manufacturing sequence.  They commonly reflect production groups, year of manufacture and/or model information as well.   The trick is having the computer separate the MSN, which is the part to be searched, from the serial number.  Some examples:

Cessna - At least 8 different serial number styles depending on model.  S/N 17280003 means series 172, production group 8, MSN 3.  S/N U20601445 means U206 series, MSN 1445.  S/N 441-0109 means model 441, MSN 109.

Piper - Pipers usually, but not always, marry the model number and year of manufacture to the MSN.  S/N 31-7900056 means model 31 manufactured in 1979, MSN 56.  However, some manufacturers start the MSN over each year so it's necessary to link the year of manufacture with the MSN to uniquely identify the airframe.  It's possible to have 2 aircraft with the same MSN, but different S/Ns (7800131 and 7900131).  There are other Piper S/N styles, but this is the most important. 

Beech/Raytheon - These aircraft have serial number ranges than span models and models that span serial number ranges.  The only way to uniquely identify an airframe is to track the serial number prefix as well as the MSN.  For example, LW-206 is an unique airframe regardless of what model it represents.  Searches have to be made of ranges within a prefix.  

Mooney - Mooney serial numbers contain production grouping, represented by a prefix, with the MSN.  Example 22-1207 is production group 22, MSN 1207.  Because MSNs may be duplicated, it is necessary to search the range within the production group prefix. 

Partenavia - This particular aircraft has some numbers where the MSN precedes the model information such as 340-02-OTC.  So it isn't safe to always take the right-most numbers as the MSN; it depends on the manufacturer.

TCM and Textron Lycoming - In contrast to other manufacturers these companies assign an MSN to an engine block that is unique irrespective of model.  Lycomings have the MSN in the center of the number such as L-18273-51A, and TCM places the MSN at the beginning, such as 321105-R.  What is really different here is that there is only one MSN 321105 regardless of the model so that it is possible to search solely by MSN without regard to model.

Carburetors, propellers, and magnetos - These each have their own serial number schemes that must be taken into consideration before a search can be made.  Bendix/TCM ADs are written against label color, of all things, since label color describes a great deal about the magneto.

Finding an AD that is N/A by S/N involves two searches.  First one by model and series only then a second by serial number.  ADs that appear in the model-series search, but not in the serial number search are N/A by S/N.  The trick here lies in the definition of series since there is no real standard to define or limit what is or isn't a series.

Searching by serial number is limited to just airframe, engine, propeller, Slick magnetos, and carburetors.  The other items on an aircraft where serial number specific ADs are written are too few to justify the labor involved in collecting numbers.  The necessary numbers are usually quite prominent in the log books and therefore easy to find if and when necessary.  But there's no sense looking unless and until you have a need to.