Tsetlin Machines are a machine learning algorithm based on propositional logic and actually quite a good match for FPGA implementation. They also train much faster than neural networks. More info: https://en.wikipedia.org/wiki/Tsetlin_machine

This Tsetlin machine is trained on the MNIST dataset and can classify digits. Included is an app that lets your draw a digit and the image to the FPGA board via USB and get the classification result back.

The Tang Nano 9K FPGA board is a very inexpensive way to get started with FPGAs - cost about $25. It's actually pretty amazing that this can fit into an FPGA this small.