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I m trying to connect a parallel LCD with microcontroller serial port via serial to parallel converter.
LCD shows random cursor blinking on different points
I think that's rather a large assumption!
In the absence of any other information, a "serial to parallel converter" could be anything that converts from any serial interface to any parallele interface.
The fact that the OP didn't think to give any further detail does suggest a high likelihood that, whatever it is, it isn't suitable for this task...