In pin-restricted microcontroller designs it is common to use analog pins and sets of resistors to encode button switch inputs to one or few pins. When a larger number of buttons is used the conventional method of encoding the buttons by resistive voltage dividers becomes complex and inaccurate. Furthermore, such design requires complex algorithm to decode the button or very accurate resistor selection.
The circuit show in the included schematic and the example code for Arduino replaces the voltage dividers by resistance-to-voltage converter implemented using simple (one resistor and two transistors) current mirror and simple array of (nRows + nColumns - 2) resistors around the switch matrix. With suitable, easily analyzed resistor values the relationship between the measured voltage and the button index becomes very linear facilitating easy decoding in SW.
For 3x4 keypad one needs 2 x 33k and 3 x 100k resistors for the key matrix and a 330k resistor for the reference current. For 4x4 keypad the corresponding values are 68k, 270k, and 1M, or alternatively 82k, 330k, and 1.2M. Any pair of close-enough C-class (beta > 400) small-signal NPN transistors will suffice.
This circuit is discussed in this video.