Found this circuit online and was wondering if it could be changed to count with a momentary switch instead of using the hall sensors?

 

You'll need to debounce the switches.

 

True. A millisecond isn't enough. Try 10 to 20 times that much capacitance.

 

The debounce circuit just using two resistors and one capacitor, but I haven't try it with op amp, the 47nF change to 1uF and 220K change to 47K, and 47K connecting to another 47K to Ground, the switch is connecting from the common pin of two 47K to 4.7K as the pin 1 of hall IC.

 

Here is a 3-digit counter with the stages already interconnected, and multiplexed displays for fewer parts.

http://www.kitsrus.com/pdf/k1.pdf

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