GATE CSE 2020 | Question: 28

Question

Consider the Boolean function $z(a,b,c)$.

 Which one of the following minterm lists represents the circuit given above?

• A. $z=\sum (0,1,3,7)$
• B. $z=\sum (1,4,5,6,7)$
• C. $z=\sum (2,4,5,6,7)$
• D. $z=\sum (2,3,5)$

Comments

finding all minterms for the expression z = a + b’c also helps in solving this problem without checking all options.

I mean z = a + b’c = a(b + b’)(c + c’) + (a + a’)b’c on simplification we get all the minterms as

===> abc, abc’, ab’c, ab’c’, ab’c, a’b’c.

---

Watch the Detailed Video Solution by clicking the button below...!

Watch Detailed Video Solution   

Must Watch the above Full Lecture to learn Combining Boolean Fuctions w.r.t. Minterms & Maxterms for all standard boolean operations. 

---

z = a + b'c

a = 100,101,110,111 = (4,5,6,7)

b'c = 001 = 101 = (1,5)

z = singa(1,4,5,6,7)

option B is correct

Answer 1

From given circuit $z=a+b'c$

K-Map for the above expression is:

Minterms are $\sum(1,4,5,6,7)$

Hence, option (B) is correct

Comments

Another way to answer without drawing K-map :----   from the diagram Z= a+b'c

for min term  a  we can write :  ab'c' (4)   ab'c (5)   abc' (6)   abc (7)   and from min term b'c we can write:   a'b'c (1)   ab'c(5)

Therefore, sigma(1,4,5,6,7)

Answer 2

z = a + b'. c

Minterms z(a,b,c) = 1,4,5,6,7

Answer 3

Option B. z=∑(1,4,5,6,7)

a + b’c

              a   b   c

  a :        1  Φ  Φ = (4,5,6,7)  [Φ = 0/1]

  b’c :     Φ  0   1 = (1,5)

=> Minterms are ∑(1,4,5,6,7)

 

Answer 4

Z = a+b’c

K MAP for the expression;

		1	1
1		1	1

     

  (1,4,5,6,7)

Answer 5

We can solve this question faster by using elimination, First we evaluate what function the circuit represents,
that is a + b'c
Then we look at the options
Options C and D both have 2 but A and B don't, so first we check if the expression is 1 at 2
2 in binary 3 bit is 010
evaluating 0 + 1' . 0
comes out to be 0, so it can't be C and D, that's for sure
Now look at A and B, see that B has 6 but A does'nt
6 in binary 3 bit is 110
putting in the values, we get 1 + 1'.0
the result comes out to be 1,
so the answer must be B, otherwise A would also have 6 which it doesn't

Answer 6

B option