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EE2301Q2F09Sol

# EE2301Q2F09Sol - University of Minnesota Department of...

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1 University of Minnesota Department of Electrical and Computer Engineering EE2301 Fall 2009 Introduction to Digital System Design L. L. Kinney Quiz II Solutions #1 1(5) Using Boolean algebra identities algebraically convert the switching function f(A, B, C, D, E, F, G) = [A + DE(F + G)][B + CD ] into a product-of-sums expression. Carefully show your derivation steps. Solution F = (A + DE)(A + F + G)(B + C)(B + D ) = (A + D)(A + E)(A + F + G)(B + C)(B + D ) 2(10) Boolean algebra identities were used to algebraically proof the identity below. For each step of the derivation, identify the Boolean algebra property by name that was used. (You do not have to identify the use of associative or commutative identities.) Solution ABD + A CD + ABD + B CD = AB(D + D ) + A CD + B CD Distributive (1 pt) = AB(1) + A CD + B CD Complementation (1 pt) = AB + A CD + B CD 0 and 1 operations (1 pt) = AB + (A + B )CD Distributive (1 pt) = AB + (AB) CD DeMorgan’s (3 pts) = AB + CD Uniting (3 pts)

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2 University of Minnesota Department of Electrical and Computer Engineering EE2301 Fall 2009 Introduction to Digital System Design
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• Fall '09
• LarryKinney
• Boolean Algebra, Elementary algebra, Algebraic structure, Boolean Algebra identities, A′CD, University of Minnesota Department of Electrical and Computer Engineering

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EE2301Q2F09Sol - University of Minnesota Department of...

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