cs281-hw2 - equations(a x’y’ xy=(xy’ x’y)’(b...

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CS281 Introduction to Computer Architecture Homework 2 Due date: Wednesday, September 17, 2008. Note: Your homework must either be typed or clearly written. I will not grade the homework if it is unreadable. AIM : To understand Boolean functions; to understand how to prove that two expressions represent the same function either by truth table or algebraic manipulation; to understand canonical forms and standard forms of Boolean function. 1. Page 118 of textbook, 3.2 (b) and (c), using truth table to prove the following equations. (b) xy’+x’y=(xy+x’y’)’ (c) xy+x’z+yz=xy+x’z 2. Page 118~119 of textbook, 3.6 (a) and (b). Using algebraic manipulation to prove the following
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Unformatted text preview: equations. (a) x’y’+xy=(xy’+x’y)’ (b) x’z+xy=x’y’z+yz+xy. 3. Page 119 of textbook, 3.7 (a). Derive the sum-of-minterms and the product-of-maxterms canonical forms for (a) F=x ⊕ y ⊕ z 4. Page 119 of textbook, 3.10 (a) and (b). Minimize the number of operators in the following Boolean expressions. (a) x’y’+xy+xy’ (b) (x+y)(x+y’) Hint for 3: ' ' xy y x y x + = ⊕ , and then you treat x’y+xy’ as one variable (e.g. w), do w XOR z again, then replace each w with (x’y+xy’). If you still have questions, come to see me during office hour or other time by appointment....
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