2 bugs of Bitcoin

Bitcoin has had 2 bugs where someone could mint as many free Bitcoin as they wanted. One bug was exploited and the other was caught in time.

Could you tell me please how those bug were exploited? I mean in the code. Since bitcoin is written in C and is immutable code... how the heck could the hacker play with the code and exploit the bitcoin network? I mean: there is no interface to play with some attack. At the best there is the bitcoin client

MY question is: techniclly where the hacker put his fancy code in order to mint more bitcoin than usual? which interface was exploited / the hacker played with in order to do that?

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