Analog to digital converter
You don't need anything as complicated as a A/D converter.  This can be done with digital logic signals easily enough.  On one side, tie each line to a digital output via a 1 k&Omega; resistor.  On the other side, tie each line high via separate 10 k&Omega; resistors, then each to its own digital input.  Then it becomes a matter of driving only one output at a time low with the others high and checking for that pattern at the other end.

This would be a lot easier to do in a microcontroller directly than to communicate all those digital inputs and outputs back to a tablet, which then runs thru this very simple algorithm. A micro can run thru the whole test nearly instantaneously in human time, so it can be doing it continually and setting a pass/fail indicator after every test.  The device would always be saying "fail" until a correct cable is plugged in, then it would pretty much instantly say "pass".

If you really needed information back to a tablet for logging or whatever, then you can use a micro with a serial port and external circuitry to provide a RS-232 connection via a DB-9 connector.  Then you can use a off the shelf USB to serial adapter to communicate between the tablet and the micro.