The ECIO28P has a 4Mhz external Xtal, not a 10Mhz one.
Setting the internal clock would make it faster, no? 48Mhz?
input portB.3/pin9 (should be Pin23) is where the pulses come into the Pic to be counted at high speed.
The bootloader does take .HEX files.. yes.. just not .bas files.
I'm not sure on the LCD screen wiring... I'll have to have another look at a wiring guide for a 1602 series LCD on ECIO28P.
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