# Documents about Prime Implicants

• 3 Pages

#### ece-301-10

George Mason, ECE 301

Excerpt: ... Plan for 1 March Midterm #1: add five points Policy: if you dispute grading of a quiz or homework, you must see me during office hours; not at end of lecture Reminder: midterm #2 on Wed, 8 March Review previous lecture (3-5; 3-6; table 3-3) Discuss other implementations (NOR-OR; NAND-AND; OR-NAND; AND-NOR) Wired OR and Wired AND Explain Table 3-4 04/26/09 ece-301 1 Plan for 1 March (contd) Dont cares Tabulation Method Prime Implicants and Essential Prime Implicants Work some problems Reading for next Monday: 4-1 to 4-3 (Adders) NOTE: lecture on Monday will spend 50% of time on review for midterm 04/26/09 ece-301 2 Tabulation Method Tedious for humans; easy for computers Works for higher dimensions Two step process: (1) determine prime implicants and (2) select the necessary prime implicants Two methods: (1) binary, or (2) decimal 04/26/09 ece-301 3 ...

• 4 Pages

#### Lecture7Note

Wisconsin, ECE 352

Excerpt: ... Lecture 7 (09/18/2002): Supplementary Note on Karnaugh-Map Instructor: Yong Kim (Section 1) During the lecture, we haven't really finished up the example on less than & equivalent relations of 4 variables K-map. Here is a example we partly covered in class with detailed explanation. Problem: Given (0, 2, 3, 5, 7, 8, 9, 10, 11, 13, 15) find all prime implicants , essential prime implicants and find a sum of product expression with minimum literals. Solution: First we find all prime implicants (rectangles containing largest number of 1's in power of 2, say one 1, two 1s, four 1s, eight 1s, .). We have total of six prime implicants : B'D', CD, B'C, BD, AB', AD) as shown below. BD 1 BD A 1 1 CD C 1 1 1 1 D 1 1 BC B AB 1 1 AD An essential prime implicant is the only prime implicant that covers a minterm or minterms. In our problem, Minterm m0 (=A'B'C'D') is covered by only one prime implicants B'D'. Thus B'D' is one of the essential prime implicants . Also Minterm m5 (=AB'C'D) is only covered by the prime ...

• 4 Pages

#### Lecture7Note

Wisconsin, ECE 352

Excerpt: ... Lecture 7 (09/18/2002): Supplementary Note on Karnaugh-Map Instructor: Yong Kim (Section 1) During the lecture, we havent really finished up the example on less than & equivalent relations of 4 variables K-map. Here is a example we partly covered in class with detailed explanation. Problem: Given ? (0, 2, 3, 5, 7, 8, 9, 10, 11, 13, 15) find all prime implicants , essential prime implicants and find a sum of product expression with minimum literals. Solution: First we find all prime implicants (rectangles containing largest number of 1s in power of 2, say one 1, two 1s, four 1s, eight 1s, ). We have total of six prime implicants : BD, CD, BC, BD, AB, AD) as shown below. BD 1 BD A 1 1 CD C 1 1 1 BC B 1 1 D AD An essential prime implicant is the only prime implicant that covers a minterm or minterms. In our problem, Minterm m0 (=ABCD) is covered by only one prime implicants BD. Thus BD is one of the essential prime implicants . Also Minterm m5 (=ABCD) is only c ...

• 15 Pages

#### quine-mccluskey-handout

Columbia, CS 6861

Excerpt: ... CSEE E6861y Prof. Steven Nowick The Quine-McCluskey Method Handout 6 January 22, 2009 Introduction The Quine-McCluskey method is an exact algorithm which nds a minimum-cost sum-of-products implementation of a Boolean function. This handout introduces the method and applies it to several examples. There are 4 main steps in the Quine-McCluskey algorithm: 1. Generate Prime Implicants 2. Construct Prime Implicant Table 3. Reduce Prime Implicant Table (a) Remove Essential Prime Implicants (b) Row Dominance (c) Column Dominance 4. Solve Prime Implicant Table Note: For this course, you are not responsible for Step #1 on this handout: the method for generating all prime implicants of a Boolean function. You can look over this method, but you will be learning, and be responsible for, a more powerful modern prime-generation technique in a few weeks. In Step #1, the prime implicants of a function are generated using an iterative procedure. In Step #2, a prime implicant table is constructed. The columns of the tabl ...