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Imagine that you want a resolution of 30 symbols/line (a very humble requirement).
Each symbol has 6 dots in horizontal line.
So it becomes 180 dots for 48uS(useful part of horisontal sweep for PAL).
The time per dot is 48/180=0.26uS.
So answer youself the question:"Is there a PIC that can output one digit each 0.26uS?"
The only way out that I can see could be to use external shift register and sync it with the PIC clock.