Chipped printer inks?

I was recently given a HP printer.Now I need ink.Looking around at prices I see that the ink cartridges are "chipped" in some way to prevent using copied cartridges I imagine.
So if I buy cheap copies that claim to be chipped and ready to go,will this block/damage the printer in anyway?
I've had mixed outcomes with this from amazon purchases although the tescos cheapies seem to do the trick.

I find it incomprehensible that more often than not its cheaper to buy an entire new printer than just replacing the ink!

That's with Epson printers.

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