You have tower, horse, knight, king, queen and pion. That 6 figures in black or white variant give you 12 figures which is a number that can fit in 4 bits. You will need 5 contacts on the bottom of each square. One with constant voltage source (like +5V or +3.3V, depending on your MCU), and four contacts that go into digital inputs of your MCU (probably via some GPIO extender chip). Each figure will then internally electrically connect +V to those 4 pins, making for each figure type a binary unique number that can be read by MCU. Polling these 4 bits in all 64 squares MCU will exactly know what figure is on what square. Everyone is licensed to use this idea for non profit goals. Commercial use of this idea costs 5000 dollars. Your move. ;-)