Hi,
When you say 'optical pulse detector' what is the application? Do you mean 'heart beat pulse' like an ECG? You will only need an ADC if the voltage is of real concern, or if you wish to store the exact waveform. If you are simply looking for 'pulses' in the analogue signal, you don't need an ADC.
Well, technically a schmit trigger, or a TTL inverter IS an ADC, it just has a resolution of 1 bit.
For counting pulses, I would use a comparator, where you set a threshold so that the output is high ('1') when its over this threshold and low ('0') when its under. Alternatively, if there is some noise in your signal, use a schmitt trigger, or at least a comparator with hysteresis. Then what you need is a frequency counter, which detects the time between the pulses and outputs the results on your LED display.
I think we need more information to be of any use. What is the application? What is the max/min frequency of these 'pulses'?
Regards,
Blueteeth