Register

GATE CSE 2004 | Question: 59

• retagged by
10,559 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
User Avatar

2 Answers

Best answer
25 votes
25 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
User Avatar
22 votes
22 votes
Answer : A.

Using K map $f = ac' + a'c$
• edited by
User Avatar
Voting & Accepting an answer helps improve the community
Answer:
← PreviousNext →
← Previous in categoryNext in category →

Related questions

33.9k
views
17 answers
81 votes
Kathleen asked Sep 18, 2014
33,949 views
GATE CSE 2004 | Question: 62
A 4-bit carry look ahead adder, which adds two 4-bit numbers, is designed using AND, OR, NOT, NAND, NOR gates only. Assuming that all the inputs ... implemented using two-level AND-OR logic.4 time units6 time units10 time units12 time units
User Avatar
19.8k
views
5 answers
46 votes
Kathleen asked Sep 18, 2014
19,817 views
GATE CSE 2004 | Question: 61
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 $X$ should be$Q_2^c$Q_2 + Q_1$\left(Q_1 + Q_2\right)^c$Q_1 \oplus Q_2$
User Avatar
7.3k
views
2 answers
26 votes
Kathleen asked Sep 18, 2014
7,276 views
GATE CSE 2004 | Question: 60
Consider a multiplexer with $X$ and $Y$ as data inputs and $Z$ the as the control input. $Z=0$ selects input $X$, and $Z=1$ selects input $Y$. What are the connections required to ... to X, R to Y, 0 to Z}$\text{R to X, 0 to Y, T to Z}$
User Avatar
12.3k
views
5 answers
27 votes
Kathleen asked Sep 18, 2014
12,301 views
GATE CSE 2004 | Question: 58
A circuit outputs a digit in the form of $4$ bits. $0$ is represented by $0000, 1$ by $0001, \ldots, 9$ by $1001$. A combinational circuit is to be designed ... NOT}$ gates may be used, what is the minimum number of gates required?$2$3$4$5$
User Avatar
Link Copied!