retagged by
10,112 views
29 votes
29 votes

Which are the essential prime implicants of the following Boolean function?

$f(a, b, c)= a' c+ ac'+b' c$

  1. $a' c$ and $ac'$
  2. $a' c$ and $b' c$
  3. $a' c$ only.
  4. $ac'$ and $bc'$
retagged by

2 Answers

Best answer
24 votes
24 votes

$f(a,b,c) = a'c+ac'+b'c$

We can write these product of sum terms into canonical product of sum form.

$f(a,b,c) = \underbrace{a'b'c}_{001}+\underbrace{a'bc}_{011}+\underbrace{ab'c'}_{100}+\underbrace{abc'}_{110}+\underbrace{ab'c}_{101}+\underbrace{a'b'c}_{001}$

$f(a,b,c) = \sum(1,3,4,5,6)$

Now, we can draw the k-map for these minterms.

  • Prime implicant of $f$ is an implicant that is minimal - that is, the removal of any literal from product term results in a non-implicant for $ f$.
  • Essential prime implicant is an prime implicant that cover an output of the function that no combination of other prime implicants is able to cover.

Prime implicants are$:a'c,b'c,ab',ac'$

Essential prime implicants are$:a'c,ac'\:\text{(green color)}$.

References:

selected by
22 votes
22 votes
Answer : A.

Using K map $f = ac' + a'c$
edited by
Answer:

Related questions

44 votes
44 votes
5 answers
2
Kathleen asked Sep 18, 2014
18,991 views
Consider the partial implementation of a $2-bit$ counter using $T$ flip-flops following the sequence $0-2-3-1-0,$ as shown below.To complete the circuit, the input $X$ sh...
24 votes
24 votes
2 answers
3