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It doesn't.

It is possible to e.g. have 32bit registers but 16bit ALU (and do 32bit operations in steps, hidden from the programmer).

This is how the 68000 worked.

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And the Z80 had a 4 bit ALU. Note that the 68000 actually had three 16 bit ALUs and could crunch 48 bits per cycle, depending on what operations you were doing since one was a full ALU while the other two more simple adders/subtractors.

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