Digital Design Lecture Notes (CSE 143) PDF

Assoc. Prof. Mohamed Moawad Abdelsalam Head of Computers Engineering and Control Systems dep., Faculty of Engineering, Mansoura University E-mail: [email protected]...

Assoc. Prof. Mohamed Moawad Abdelsalam Head of Computers Engineering and Control Systems dep., Faculty of Engineering, Mansoura University E-mail: [email protected] Lecture 4 Simplify the following Functions  Canonical standard form 1. Minterms Any Boolean function can be represented as a sum of minterms The minterms can be labeled as (m) The minterms deals with logic (1) The minterm is a term that contains all the function variables (Anded) together. F = ∑m For AND gate : F= m3 For OR gate: F=m1+m2+m3 = ∑m1,m2,m3 = ∑(1,2,3) 6 Express the Boolean function F= A+B’C as a sum of minterms F= A+B’C F= A(B+B’) + B’C(A+A’) F=AB+AB’+AB’C+A’B’C F=AB(C+C’)+AB’(C+C’)+AB’C+A’B’C F=ABC+ABC’+AB’C+AB’C’+AB’C+A’B’C F=ABC+ABC’+AB’C’+AB’C+A’B’C F=m7+m6+m4+m5+m1 F(A,B,C)=∑(1,4,5,6,7) Express the Boolean function as a sum of minters F1(A,B,C)=∑(1,4,5,6,7) F2(A,B,C)=∑(1,3,4,5)  2. Maxterms Any Boolean function can be represented as a product of maxterms The maxterms can be labeled as (M) The maxterms deals with logic (0) The maxterm is a term that contains all the function variables (ORed) together. F = ∏M For AND gate : F= M0.M1.M2= ∏(M0,M1,M2)= ∏(0,1,2) For OR gate: F=M0 Express the Boolean function F= A+B’C as a product of maxterms F= A+B’C F= (A+B’)(A+C) F=(A+B’+CC’)(A+C+BB’) F=(A+B’+C)(A+B’+C’)(A+B+C)(A+B’+C) F=(A+B’+C)(A+B’+C’)(A+B+C) F=M2.M3.M0 F(A,B,C)=∏(0,2,3) Therefore m = M’ 4. NAND gate F=(A.B)’ = A’+B’ 2. NOR gate F=(A+B)’ =A’.B’ Implement gates using NAND 14 Implement gates using NOR 15