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From Jimmy Du's Essential Chinese, p. 46:
I understand everything you say. 你说的我都懂。
I don't understand all they say. 他们说的我不是都懂。
Why is 不是 there in the second example, and not simply 不? I have only seen 懂 used as a verb before. This does not resemble anything I have learned.
You can say "他們說的我不都懂". It's just far less common than "他們說的我不是都懂" nowadays. As user6065 said, "不"/"不是" is used to modify "都" (= "all").
I understand everything they say. 他们说的我都懂。
I don't understand all they say. (I only understand some of what they say.)
他们说的我不都懂。or 他们说的我不是都懂。Here using 不 or 不是 makes no differences.
I don't understand anything they say. 他们说的我都不懂。
So 不都 means not all, ie maybe some, and 都不 means all not, ie none.
