Question

(a) List all seven product term implicants of F(a, b, c) = Σ m(0, 1, 5, 7) Which of these implicants are prime? Why is a′c not an implicant? (b) Defne a prime implicant. (c) Why must every term in a minimum sum-of-products expression be a prime implicant? Check your answer using a Karnaugh map. 170 Unit 6 (d) Given that F(A, B, C, D) = Σ m(0, 1, 4, 5, 7, 10, 15), which of the following terms are not prime implicants and why? A′B′C′ A′C′ BCD ABC AB′CD′ 4. Study Section 6.2, The Prime Implicant Chart. (a) Defne an essential prime implicant. (b) Find all of the essential prime implicants from the following chart. ab c d 0 4 5 10 11 12 13 15 (0, 4) 0 – 0 0 × × (4, 5, 12, 13) – 1 0 – ×× × × (13, 15) 1 1 – 1 × × (11, 15) 1 – 1 1 × × (10, 11) 1 0 1 – × × m4 m5 m7 m13 P1 bd ×× × P2 bc′ ×× × P3 a′b ××× P4 c′d × × We will fnd all minimum solutions using Petrick’s method. Let Pi = 1 mean the prime implicant in row Pi is included in the solution. Which minterm is covered iff (P1 + P3) = 1?_________ Write a sum term which is 1 iff m4 is covered._________ Check your answer using a Karnaugh map. (c) Why must all essential prime implicants of a function be included in the minimum sum of products? (d) Complete the solution of Table 6-5. (e) Work Programmed Exercise 6.1. (f ) Work Problems 6.2 and 6.3. 5. Study Section 6.3, Petrick’s Method (optional). (a) Consider the following reduced prime implicant chart for a function F: Quine-McCluskey Method 171 Write a product-of-sum terms which is 1 iff all m4, m5, m7 and m13 are all covered: P = ____________________________________________________________ (b) Reduce P to a minimum sum of products. (Your answer should have four terms, each one of the form PiPj .) P = ____________________________________________________________ If P1P2 = 1, which prime implicants are included in the solution?_________ How many minimum solutions are there?________ Write out each solution in terms of a, b, c, and d. (1) F = (2) F = (3) F = (4) F = 6. Study Section 6.4, Simplifcation of Incompletely Specifed Functions. (a) Why are don’t-care terms treated like required minterms when fnding the prime implicants? (b) Why are the don’t-care terms not listed at the top of the prime implicant chart when fnding the minimum solution? (c) Work Problem 6.4. (d) Work Problem 6.5, and check your solution using a Karnaugh map. 7. If you have LogicAid or a similar computer program available, use it to check your answers to some of the problems in this unit. LogicAid accepts Boolean functions in the form of equations, minterms or maxterms, and truth tables. It fnds simplifed sum-of-products and product-of-sums expressions for the functions using a modifed version of the Quine-McCluskey method or Espresso-II. It can also fnd one or all of the minimum solutions using Petrick’s method. 8. Study Section 6.5, Simplifcation Using Map-Entered Variables. (a) For the following map, fnd MS0, MS1, and F. Verify that your solution for F is minimum by using a fou

Answer 1

Answering first part of the question