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20 votes
20 votes

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

  1. independent of one variable
  2. independent of two variables
  3. independent of three variable
  4. dependent on all the variables

2 Answers

Best answer
25 votes
25 votes

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

edited by
11 votes
11 votes

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'DCDCD'
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 .
 

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