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> Multiplications/divisions need to be hand-rolled.

In the context of someone's first contact with assembly language, that's a good thing! Translating various multiplication and division algorithms to assembly is a great way to learn it.

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I learned to implement my own multiplication and division as part of learning bignum with a high level language (in my case Pascal). By the time I learned assembly language I simply focused on how to translate high level language to assembler; basically be a manual compiler and compare my output against a real compiler.

It seems unnecessary to learn any algorithm including the multiplication algorithm in assembly language.

Implementing shift-and-add multiplication and division algorithms in assembly, and analyzing them, is a very formative exercise in my experience.

Besides, if assembly language is good enough for Knuth to express all the algorithms in TAOCP, it's good enough for me...

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