3. Write down a list of all 16 zero-one sequences of length four starting with 0000 in such a way that each entry differs from the previous one by changing just one digit. This is called a Gray Code. Thatis, a Gray Code for 0-1 sequences of length n is a list of the sequences so that each entry differs from the previous one in exactly one place. Can you describe how to get a Gray Code for 0-1 sequences of length five from the one you found for sequences of length 4? Can you describe how to prove that there is a Gray code for sequences of length n?

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Such lists are usually written vertically, with each binary sequence (“word”) in a line.
However, to explain how the principle works, it can be more convenient to write the words (sequences) vertically, so the listing of the words is horizontal, and so we shall do here.
To obtain the usual form of writing we can simply rotate what is written here by 90 degrees.

Also for convenience we name “1-digit rule” the rule that only 1 digit is different between two consecutive words.

Let us start with words one digit long: There are only two of these: 01...

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