Does a computer chip get rendered useless if one transistors gets damaged?

Does an computer chip get rendered useless if one transistors gets damaged or placed incorrectly? 

Not necessarily. See, oddly enough, making a processor (as we're specifically discussing a chip made from transistors) is not an exact science.
cpu transistors gets damaged
processor are making en masses in a wafer of silicon, and even though the CPU
is making those hundred or so CPUs is identical,
 material imperfections and plain dumb luck can mean that one chip might be an extremely powerful and stable example,
 but the one next to it, despite being technically identical, can't achieve as much.

There is a concept known as "binning" in the CPU production industry,

where the same technical layout produces chips of unequal performance. 
The best of the best get labeled and priced at the top of the market.
 Less capable ones get marked down and sometimes even have transistors fused to block off capabilities that are unstable or broken in the lesser model.
 Separating these technically identical but differently performing CPUs into different tiers is called binning.
And of course, sometimes the imperfections are so great as to make the product unusable.
 A decent yield is around 70%+ usable,saleable products,
with 80% and above being generally bare minimum as far as the mainstream is concerned.
 As an aside, this is also why miniaturization of transistors and die sizes are so important - if you can only fit ten dies in a wafer and have two of them be bad, that's 20% loss.
 But if you can fit 100 in, then even if 10 are bad, you've still got 90% yield.

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