kmap problem

Question

for n variable kmap combining 16 cells canaining 1's as a single group will result a terms of __________ litrals
a.4
b.n-4
c.n+4
d.4n

Comments

what is the answer?

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b.n-4

Answer 1

Try with n variable and 8 1's :

We get n - 2³( here # is variable) = so here solution n-3= 1 variable as answer i.e. z' .

Try with n variable and 16 1's :

Here solution need 0 variable which is n - 2⁴ = n-4 = 0

Answer 2

We should do it like this:

Assume we have 4 variable K map. Now if we merge all the 16 cells of this K map we get the function as 1 which is free from all the 4 variables.

Now we can use this to generalize for n variables . If we are able to merge 16 adjacent cells of the K map of n variables hence we will have expression of n-4 variables or we can say n-4 literals.

Hence B should be the correct option.