Discussion
Design a K-Map for F(x, y, z) = \(x\overline{z} + xyz + y\overline{z}\) of F(x, y, z) and find prime implicants.
Answer: A
The prime implicants are \(xy,\ y\overline{z},\ x\overline{z}\).
Expand each term into minterms (x y z as a binary number): \(x\overline{z}\) gives 100 and 110, \(xyz\) gives 111, and \(y\overline{z}\) gives 010 and 110. So F = m(2, 4, 6, 7).
On the K-map, 6 and 7 pair as \(xy\), 2 and 6 pair as \(y\overline{z}\), and 4 and 6 pair as \(x\overline{z}\). None of these can be enlarged further, so all three are prime implicants (and all are essential).
Single literals x, y, z would cover cells where F is 0, and the terms \(\overline{x}y\), \(yz\), \(x\overline{y}\), \(\overline{x}z\) each include a 0 cell such as 011, 001 or 101.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development