GATE IT 2008 | Question: 8

Question

Consider the following Boolean function of four variables

$f(A, B, C, D) = Σ(2, 3, 6, 7, 8, 9, 10, 11, 12, 13)$

The function is

• A. independent of one variable
• B. independent of two variables
• C. independent of three variable
• D. dependent on all the variables

Comments

I calculated min-term from K-map

F = AC' + A'C + B'C

So function  F depend on  A,B, C not D

it means Function independent one variables

Option (A) is correct answer

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If we change the order of variables in rows and columns for example instead of AB/CD if we use CD/AB  and then construct a kmap then the answer is different , then the expression is depenedent of all the variables.. does changing the order of variables affects the answer if yes which way is correct ..

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Order really doesn't matter. Either way you'll get the same answer.

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There are 2 minimal SOP expressions for the given boolean function, in both of them, $f$ is independent of the boolean variable $d$.

 

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i think the msop should be : A'C + AC' + AB'

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Answer 1

$$ \underset{\large{y=\bar AC+\bar BC + A \bar C}}{\begin{array}{cc}(2,3,6,7)&:\bar A C \\ (2,3,10,11)&:\bar B C \\ (8,9,12,13)&:A \bar C \\ \hline\end{array}}$$
Option A.

Comments

there is another selection which will also give independent of one variable

(8,9,10,11) AB^ +(8,9,12,13) AC^ + (2,3,6,7) A^C             //here "^" symbole used for complement

answer: (A)

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It is dependent on three variable and independent of one variable .

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@Aditi Tiwari why have you not taken (8,9,10,11) as prime implicant?

Answer 2

Given the following Boolean function of four variables

f(A, B, C, D) = Σ(2, 3, 6, 7, 8, 9, 10, 11, 12, 13)

 using K-map , 
 

	C'D'	C'D	CD	CD'
A'B'			1(3)	1(2)
A'B			1(7)	1(6)
AB	1(12)	1(13)
AB'	1(8)	1(9)	1(11)	1(10)

 So , the output function is f(A,B,C,D)
f  =  A'C + AC' + AB'

function f is dependent on A , B and C , 
and function f is independent on D only , 
hence option (A) is TRUE .