Digital Logic circuits class material for EEE

Digital Logic circuits

1. Lecture 3 UEE3303 Digital Logic Circuits 1 Dr. V Thiyagarajan Associate Professor Department of Electrical and Electronics Engineering Sri Sivasubramaniya Nadar College of Engineering Chennai, Tamil Nadu, INDIA – 603 110

2. CANONICAL AND STANDARD FORMS 2

3. MINTERM 3 When a Boolean function or logical expression is expressed in the SSOP (Standard Sum of Product) Form or canonical form, then each term of the expression is called a  minterm . In other words, a product term of a logical expression in n variables, which contains each of the n variables in its either complemented or un-complemented form is called a  minterm . A minterm is often represented as mi, where, i is an integer in between 0 and 2 (n-1) . Here, "n" is the number of variables in the expression. Therefore, minterms can be denoted as m , m 1 , m 2 ,m 3 ,... Here, the suffixes the decimal codes of the combinations of variables. In a minterm , a variable will appear in its complemented form if its value is equal to 0. And, the variable will appear in its un-complimented form if its value is equal to 1.

4. MINTERM 4 For a logical expression in 2-variables (A and B), the possible minterms are, For a logical expression in 3-variables (A, B, and C), the possible minterms are,

5. MAXTERM 5 When a Boolean function or logical expression is expressed in the SPOS (Standard Product of Sum) Form or canonical form, then each term of the expression is called a  maxterm. In other words, a sum term of a logical expression in n variables, which contains each of the "n" variables in its either complemented or un-complemented form is called a  maxterm. The maxterm is often represented by Mi, where " i " is an integer between 0 and 2 (n-1) . Here, "n" is the total number of variable in the logical expression. Therefore, maxterms of a logical expression can be denoted as M , M 1 , M 2 , ... where the suffixes represent their decimal codes of the combinations. In the case of maxterms, a variable will be written in its complemented form if its value is equal to 1, and the variable will be written in its un-complemented form if its value is equal to 0.

6. MAXTERM 6 For a Boolean function in 2 variables (A and B), the possible maxterms are, For a Boolean expression in 3 variables (A, B, C), the possible maxterms are,

7. Example - 1 7

8. Example - 1 8

9. MINTERM and MAXTERM 9

10. 10 MINTERM and MAXTERM The important characteristics of minterms and maxterms are described as follows: For a given combination of n-variable values, only one of 2n minterms is equal to 1 while only one of 2n maxterms is equal to 0. The sum of all minterms is equal to 1; the product of all maxterms is equal to 0. The product of any two minterms is equal to 0; the sum of any two maxterms is equal to 1. A minterm is equal to the complement of its corresponding maxterm and a maxterm is equal to the complement of its corresponding minterm .

11. 11 SOP vs POS Feature SOP ( Sum of Products) POS ( Product of Sums) Logic Structure OR of multiple AND terms AND of multiple OR terms Based On Minterms (Output = 1 in truth table) Maxterms (Output = 0 in truth table) K-Map Grouping Group 1’s Group 0’s Use in Truth Table Includes rows where output is 1 Includes rows where output is Circuit Implementation AND-OR logic circuits OR-AND logic circuits Output is 1 when... Any one product term is true All sum terms are true Example F = A̅BC̅ + AB̅C + ABC̅ F = (A + B + C̅)(A̅ + B + C)(A + B̅ + C)

12. Example - 2 12 Obtain the canonical sum of product form of the following function.  

13. Example - 3 13 Obtain the canonical sum of product form of the following function  

14. Example - 4 14

15. Example - 5 15 Obtain the canonical product of the sum form of the following function.  

16. Example - 6 16 Obtain the canonical product of the sum form of the following function.  

17. Example - 7 17

18. Example - 8 18 Derive a truth table for the SOP expression

19. References Morris Mano. M, “Digital Logic and Computer Design”, Prentice Hall of India, 3rd Edition, 2005. Donald D. Givone , “Digital Principles and Design”, Tata McGraw Hill, 1st Edition, 2003. Tocci R.J., Neal S. Widmer, “Digital Systems: Principles and Applications”, Pearson Education Asia, 12th Edition, 2017 Donald P Leach, Albert Paul Malvino , Goutam Sha, “Digital Principles and Applications”, Tata McGraw Hill, 7th Edition, 2010. Thomas L Floyd, “Digital fundamentals”, Pearson Education Limited, 11th Edition, 2018. 19

20. 20 Thank You