EECE 320 Homework 2, Fall 2011

American University of Beirut Department of Electrical and Computer Engineering EECE 320 – Digital Systems Design Dr. Lama Hamandi Assignment 2 due 17/10/2011 1) Prove the following identity using a truth table: A’ + AX’Y + AXZ + AYZ = A’ + X’Y + XZ 2) Obtain the truth table of the following function and express it in canonical sum of minterms, the ∑ notation, canonical product of maxterms, the ∏ notation. F = A’ + AX’Y + AXZ + AYZ 3) Minimize the following functions to a minimum sum of product using rules of Boolean algebra: a- F(X, Y, Z) = ∑m(0,2,4,6) b- F(X, Y, Z) = ∑m(1,2,3,7) c- F(X, Y, Z) = ∑m(1,2,3,6,7) d- F(W,X,Y,Z) = Σ(0,4,5,6,7,8,14,15) Then draw them using AND, OR, inverter gates. 4) Minimize the following functions to a minimum product of sums using rules of Boolean algebra: a- WX(Z+XZ’) + X(Y+Y’WZ) b- (X’Y + XY’)(WX+W’X’)+(WY)’ 5) Analyze the following circuit and express g as a minimal sum of product expression.