84 2.1 ENS 220 - INTRODUCTION TO COMPUTER ENGINEERING HOMEWORK 2: BOOLEAN ALGEBRA AND LOGIC GATES Complete the following questions. Submit the homework as either a collection of images, or a single pdf file. Demonstrate the validity of the following identities by means of truth tables: (2) DeMorgan's theorem for three variables: (x + y + z)' - *'y'r' and (xy) - *' + y + 3 (b) The distributive law.x+yz = (x+y)(x+2) (c) The distributive law.xly + 2) xy + x (d) The associative law.x+y+z) = (x+y)++ (c) The associative law and xyz) = (xy) 2.4 Reduce the following Boolean expressions to the indicated number of literals: (a)" A'C + ABC + AC to three literals (b) (xy + 2) + 3 + xy + wz to three literals 2.7 Draw logie diagrams of the circuits that implement the original and simplified expressions in Problem 2.4 2.11 List the truth table of the function (b) F-betale 2.13 Draw logie diagrams to implement the following Boolean expressione (a) -(+2) (b) (y) - 2.22 Converseach of the following expens into sum of products and product of some (W 2.27 Write the Boolean equations and draw the logic diagram of the circuit whose outputs are defined by the following truth table: Table P2.27 6 b c 0 1 0 1 1 1 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 D 2.28 Write Boolean expressions and construct the truth tables describing the outputs of the circuits described by the logic dingrats in Fig. P2.28 FIGURE P228 ) CH VOBOOT