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I'm trying to understand how a simple hex string like 0x25d8dcf2 is enough information to execute a function in a contract. I've read up on the ABI and understand that the hex string is basically just a hash of the function signature, but how is it determined that this piece of data will end up jumping to the appropriate address for that function in the bytecode of the contract?

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It's the job of the compiler to produce the correct EVM bytecode so that as you say the MethodID "piece of data will end up jumping to the appropriate address for that function in the bytecode of the contract".

Since the MethodID is only 4 bytes, hash collisions (between 2 different functions) are possible. The Solidity compiler gives an error in that case and will not produce any bytecode at all.

If this helps, for conceptual purposes only, here is a very rough example of the bytecode that an EVM compiler would produce:

method_id = first 4 bytes of msg.data
if method_id == 0x25d8dcf2 jump to 0x11
if method_id == 0xaabbccdd jump to 0x22
if method_id == 0xffaaccee jump to 0x33
other code
0x11:
code for function with method id 0x25d8dcf2
0x22:
code for another function
0x33:
code for another function

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