Homework 2 Solutions for Computer Architecture I Logic and Computer Structures | CS 266, Study notes of Computer Architecture and Organization

Download Homework 2 Solutions for Computer Architecture I Logic and Computer Structures | CS 266 and more Study notes Computer Architecture and Organization in PDF only on Docsity! University of Illinois at Chicago CS 266: Computer Architecture I Fall 2012 Homework 2 Solutions Question 1 Demonstrate by means of truth tables the validity of the following identities:  (a) [10] ̅ ̅ ̅ ̅ ̅ 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 1  0  0 0 0 1 1 0 0 0 1  0  1 0 1 0 1 0 0 0 1  1  0 1 0 1 1 0 1 0 1  1  1 1 0 0 0 1 1 0 (b) [10]             0 0 1 1 0 1 1 1 1 0 1 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 0         1 1 0 0 1 0 1 1 1   Question 2 Prove the identity of the following Boolean equations using algebraic manipulation:  (a) [10] ̅ ̅ ̅ ̅ ̅ ̅ ̅ 1 ̅ ̅ ̅ 1 ̅ ̅ (b) [10] ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ Question 3 Find complement: (You do not have to simplify):  (a) [5] X Y Z   (b) [5]   ̅ ̅   Question 4 Simplify the following Boolean equations using Boolean theorems. Check the correctness using a truth table.  (a) [10] ̅ ̅ ̅ ̅       ̅  ̅  ̅  ̅  ̅ 1  1  1  0  0  0 0 1 1 1  1  0  0  0  1 1 0 1 1  0  1  0  1  0 0 1 1 1  0  0  0  1  1 0 0 0 0  1  1  1  0  0 0 0 1 0  1  0  1  0  1 0 0 1 0  0  1  1  1  0 0 0 1 0  0  0  1  1  1 0 0 0   (b) [10] ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ 1 ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ 0 0 0 0 1 1 1 1 0 0 0 1 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 0 1 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 1 0 0 0 0 1 0 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 1 0 0 0 1 1