Because real life solutions aren't pretty or well thought out all the time so students shouldn't expect them 
So here's a question for you all. Why the hell do textbook descriptions of a 1-bit output ΔΣ modulator show stuff like the first image, when the second image produces *literally identical output* and is way easier to understand?pic.twitter.com/ri3RrFXZok
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That is to say, theory vs application?
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I imagine that it is easier to calculate with the first one than with the second one. I don't need to think a lot to write down the first one as a Z equation but for the second one I need to think twice. Never the less the second one is easier to understand.
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You definitely need to think to write the first one as anything - the bit size and encoding shenanigans are much harder to reason about than the second version. Now the *topology* would make sense if they dropped all that junk and just wrote the lower path as negative feedback.
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I think both images suck, because for *understanding* the principle you shouldn't bother with things like word lengths at all.
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And if you first understand Delta Modulation, you can both understand ADPCM *and* ΣΔ modulation.
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I guess, some people may like to see the whole thing in more detail. You are right though, when it comes to learning the basics, the one on the left is just overkill.
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But... it isn't the whole thing in "more" detail. It's just stupid. It's a completely ridiculous digital implementation of the concept. The *topology* on the left may make sense for analysis purposes, but the specifics of the implementation shown do not.
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