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I need help about this exercise:

Which rows and which columns of a 4 x 16 map for
Boolean functions in six variables using the Gray codes
1111, 1110, 1010, 1011, 1001,1000,0000,0001, 0011, 0010,
0110,0111, 0101,0100, 1100, 1101 to label the columns
and 11, 10, 00, 01 to label the rows need to be considered
adjacent so that cells that represent minterms that differ
in exactly one literal are considered adjacent?

As i thought, adjacent rows should be 11 and 10, 10 and 00, 00 and 01, 11 and 01.. Similarly I thought the same thing about the columns, however, the solution is:

Rows 1 and 4 are considered adjacent.
The pairs of columns considered adjacent are: columns 1 and
4, 1 and 12, 1 and 1 6, 2 and 1 1,2 and 15, 3 and 6, 3 and 1 0, 4
and 9, 5 and 8, 5 and 1 6, 6 and 1 5, 7 and 1 0, 7 and 14, 8 and
13, 9 and 12, 11 and 14, 13 and 16.

I just don't get why is it like that

If someone has some time and will to help me I would be more than grateful !! Thanks :)

[Tags might need to be edited, couldn't put anything in connection to boolean funcions etc.]

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    How about drawing a K-Map? – 2017-02-14
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    @Bram28 That got me even more confused. It says 4 x 16 in the exercise, however K-map with 6 variables should be 8 x 8. – 2017-02-14
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    It doesn't have to be 8 x 8, it could indeed be 4 x 16 ... you just have to be careful about the groupings, since groups can be formed that are not necessarily physically adjacent in the map ... but this is exactly what the question is asking! That is: Which rows and columns are 'logically adjacent' even though they are not 'physically adjacent'? And for this, simply look at the Gray codes, e.g. columns 1 and 4 are adjacent because their Gray codes (1111 and 1011) differ by just 1 bit. – 2017-02-14
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    @Bram28 Couldn't tag u down – 2017-02-14

1 Answers 1

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The rows 11 and 10 are indeed adjacent, but they don't need to be explicitly labeled as adjacent, since in the K-Map they are already physically adjacent. So: the question is asking which rows (and columns) you need to label as adjacent (because their Gray codes differ by only 1 bit) when they are not physically adjacent. So for the rows, that is only row 1 (11) and 4 (01).

For the columns, just to give an example: column 1 has Gray code 1111, and column 4 has Gray code 1011. So: they differ by only 1 bit, meaning they are logically adjacent .. but they are not physically adjacent. So, you need to label them as adjacent.

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    I think I do understand so from the above.. row 1 (11) and row2 (10) are physically adjacent, however they are asking for those which are logically adjacent. Those are row 1 (11) and row 4 (10). Same for columns.. Probably got confused by the fact that it wasn't explicitly said ? Or was it ? – 2017-02-14
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    @MathNewbie I think they tried to say it with the 'need to be considered adjacent' phrase ... presumably physically adajcent rowns and columns don't 'need to be considered' since they are already adjacent .... But I agree: they certainly could have been a lot more clear about that! – 2017-02-14
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    You're welcome! :) – 2017-02-14