hw2 - Prof. M. Mansour American University of Beirut...

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Prof. M. Mansour American University of Beirut Department of Electrical and Computer Engineering EECE 320 – Digital Systems Design Summer 2009 Homework 2 (Due Friday July 10 in class) Problem 1 [10 pts] : Construct a logic circuit that performs the XOR operation using AND gates and inverters only. Problem 2 [10 pts] : Reduce the following Boolean expressions to the indicated number of literals: a) ( x y ’ + z )’ + z + xy + wz to three literals b) A B ( D ’ + C D ) + B ( A + A CD ) to one literal c) ( A ’ + C )( A ’ + C ’)( A + B + C’D ) to four literals Problem 3 [10 pts] : Implement the function F = xy + x y ’ + y x a) Using AND, OR, inverters b) Using OR and inverters only c) Using AND and inverters only Problem 4 [10 pts] : Given the Boolean function F = xy z + x y z + w xy + wx y + wxy . Draw the logic diagram of F . Then simplify F to the minimum number of literals using Boolean algebra. Draw the logic diagram of the simplified function and compare the total number of gates with the previous logic diagram. Problem 5 [10 pts] : Prove the identity of the following Boolean equations using algebraic manipulation : a) bd + ac d ’ + abc ’ + a bc + b cd ’ = bd + ac d ’ + a cd ’ + ab d b) ( a ’ + b ’ + c + d’ )( a + b + c ’ + d ) = cd + ab ’ + ac + a c ’ + a b + c’d’ Problem 6 [10 pts] : Express the following functions in sum-of-products and product-of-sums forms: a) ( XY + Z )( Y + XZ ) b) ( A ’ + B )( B ’ + C ) c) WXY ’ + WXZ ’ + WXZ + YZ Problem 7 [10 pts] : Simplify the function using algebraic manipulation . = D
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This note was uploaded on 09/07/2010 for the course FEA eece320 taught by Professor Unknown during the Spring '10 term at American University of Beirut.

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hw2 - Prof. M. Mansour American University of Beirut...

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