14 votes 14 votes Consider the Boolean function $z(a,b,c)$. Which one of the following minterm lists represents the circuit given above? $z=\sum (0,1,3,7)$ $z=\sum (1,4,5,6,7)$ $z=\sum (2,4,5,6,7)$ $z=\sum (2,3,5)$ Digital Logic gatecse-2020 digital-logic canonical-normal-form 2-marks + – Arjun asked Feb 12, 2020 retagged Nov 30, 2022 by Lakshman Bhaiya Arjun 7.9k views answer comment Share Follow See all 3 Comments See all 3 3 Comments reply Shubham Shukla 6 commented Feb 19, 2020 reply Follow Share making a truth table would have been easy and quick to answer this question.. 2 votes 2 votes IamDRD commented Jan 17, 2021 reply Follow Share draw truth table 5 votes 5 votes Raju Kalagoni commented Jun 8, 2023 reply Follow Share 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. 0 votes 0 votes Please log in or register to add a comment.
Best answer 18 votes 18 votes 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 Ashwani Kumar 2 answered Feb 12, 2020 selected Feb 12, 2020 by Prashant. Ashwani Kumar 2 comment Share Follow See 1 comment See all 1 1 comment reply Srinivas_Reddy_Kotla commented Feb 12, 2020 i edited by Srinivas_Reddy_Kotla Feb 12, 2020 reply Follow Share 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) 5 votes 5 votes Please log in or register to add a comment.
6 votes 6 votes z = a + b'. c Minterms z(a,b,c) = 1,4,5,6,7 Shaik Masthan answered Feb 12, 2020 Shaik Masthan comment Share Follow See all 0 reply Please log in or register to add a comment.
3 votes 3 votes 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) Madhav answered Sep 6, 2020 Madhav comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes Z = a+b’c K MAP for the expression; 1 1 1 1 1 (1,4,5,6,7) Ronak.e3 answered Nov 17, 2020 Ronak.e3 comment Share Follow See all 0 reply Please log in or register to add a comment.