K-Maps Prime Implicates and Essential Minterms

  • Thread starter Extreme112
  • Start date
  • Tags
    Prime
In summary, the conversation discusses how to draw k-maps for functions with "don't care" conditions and how to simplify them using SOP and POS. The methods for circling essential prime minterms and indicating prime and essential implicants are also described. The speaker also mentions that for the second function, there are multiple ways to circle the 1's, but the best approach is to encircle the largest possible circles for a simplified solution.
  • #1
Extreme112
5
0

Homework Statement


For each of the following functions with “don’t care” conditions, draw two k-maps: one for the simplified SOP and the other for the simplified POS; circle the essential prime circles, and underline the essential prime minterms (maxterms) as described in lecture. Indicate all prime implicants (implicates) and all essential implicants (implicates).
(a) F(w,x,y,z) = ∑m (0,2,4,6,7,8,12,13), d(w,x,y,z) = ∑m (5,10)

Homework Equations


...

The Attempt at a Solution


IMG_20150212_201902.jpg

I just want to check if my answers are correct. First one seems like all 0's are essential. And the second one it seems like there are many ways to circle the 1's.
 
Physics news on Phys.org
  • #2
to get a more simplified answer we encircle the 1s or 0s with as many same bits(adjacent to it) as possible. So, by this I mean that the best way is to encirlce the largest circles possible. For example, if there are combinations of QUAD and BIN possible, then we essentially choose the QUAD, thereby obtaining a simplified solution.
 

Related to K-Maps Prime Implicates and Essential Minterms

1. What are K-Maps and how are they used in science?

K-Maps, short for Karnaugh Maps, are a graphical method used for simplifying Boolean algebra expressions. They are often used in computer science and engineering to help simplify complex logic circuits and reduce the number of gates needed for a circuit.

2. What are prime implicants in K-Maps?

Prime implicants are the largest possible groups of adjacent cells in a K-Map that can be combined to create a simplified Boolean expression. They are essential in finding the most efficient solution for a logic circuit.

3. How are essential minterms determined in K-Maps?

Essential minterms are identified by looking at each prime implicant and determining which minterms (or input combinations) are covered by that implicant. Any minterms that are only covered by one prime implicant are considered essential minterms and must be included in the simplified expression.

4. Can K-Maps be used for expressions with more than four variables?

Yes, K-Maps can be used for expressions with up to six variables. However, as the number of variables increases, the size and complexity of the K-Map also increases, making it more difficult to visually identify prime implicants and essential minterms.

5. Are there any limitations to using K-Maps for simplifying Boolean expressions?

While K-Maps are a powerful tool for simplifying Boolean expressions, they do have some limitations. They can only be used for expressions with AND and OR operations, and they do not take into account the physical limitations of a logic circuit, such as propagation delays and fan-out. Additionally, K-Maps may not always provide the most optimal solution for a logic circuit.

Similar threads

Optimizing K-Map Solution for Prime Implicants
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Question about finding min. sum of product using K-maps?
    • Engineering and Comp Sci Homework Help
Replies
1
Views
2K
Comp Sci Write the predicate formulas for the given predicates
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Magnetic field at origin due to infinite wires and semicircular turn
    • Introductory Physics Homework Help
Replies
3
Views
1K
Array-list implementation of tree problem
    • Engineering and Comp Sci Homework Help
Replies
3
Views
2K
MHB Quine-McCluskey method: Prime implicants - disjunctive minimal forms
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
Simplify & K-Map Homework Statement
    • Engineering and Comp Sci Homework Help
Replies
5
Views
5K
[Pumping Lemma] About the cases for y in the xy^iz criterion
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Engineering Two-level NAND circuits plus ROM?
    • Engineering and Comp Sci Homework Help
Replies
1
Views
1K
Engineering Simplifying switching circuit literals
    • Engineering and Comp Sci Homework Help
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top