How can I convert a continuous signal like a switch to a singular pulse for the 555 count and not be obstructed while counting.
That's what a Schmitt trigger can be used for.
Since you can't use any more ICs then the a crude implementation with transistors can still be an option:
simulate this circuit – Schematic created using CircuitLab
The circuit above will output a virtually-zero-width positive pulse. The pulse width can still be adjusted with the resistors but if you want to get a meaningful pulse e.g. 1 ms (I don't know actually, depends on the application) then you can use an alternative pulse generator:
simulate this circuit
The pulse width can be adjusted with RT and CT. You can place this block to the 555's TR input:
simulate this circuit
The good thing with this circuit is that even if the switch is left closed indefinitely the circuit will generate only one pulse. To generate another pulse, the switch must be released and then pressed again.
The bad thing is that there's no protection against switch bouncing i.e. if a bouncing happens that'll reflect to the output. But the 555 is immune anyways so shouldn't be a problem for your application.
I can't use IC
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