reference-sheet2 - (x + y)(x + y’) = x Adjacency x +...

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Reference Sheet You may separate this sheet from the exam, but please hand it in with your exam. Please do not include work on this page. Boolean Algebra x + 0 = x x 1 = x Identity x + 1 = 1 x 0 = 0 Dominance x + x = x x x = x Idempotent x + x’ = 1 x x’ = 0 Complement (x’)’ = x Double Complement x + y = y + x xy = yx Commutative x + (y + z) = (x + y) + z x(yz) = (xy)z Associative x(y + z) = xy + xz x + yz = (x + y)(x + z) Distributive (x + y)’ = x’y’ (xy)’ = x’ + y’ DeMorgan’s x + xy = x x (x + y) = x Absorption xy + xy’ = x
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Unformatted text preview: (x + y)(x + y’) = x Adjacency x + x’y = x + y x(x’ + y) = xy Adsorption xy + x’z + yz = xy + x’z (x + y)(x’ + z)(y + z) = (x + y)(x’ + z) Consensus Flip-Flop Tables Characteristic D Q(t+1) 0 0 1 1 J K Q(t+1) 0 0 Q(t) 0 1 0 1 0 1 1 1 Q’(t) S R Q(t+1) 0 0 Q(t) 0 1 0 1 0 1 1 1 X T Q(t+1) 0 Q(t) 1 Q’(t) Excitation Q(t) Q(t+1) D 0 0 0 0 1 1 1 0 0 1 1 1 Q(t) Q(t+1) J K 0 0 0 x 0 1 1 x 1 0 x 1 1 1 x 0 Q(t) Q(t+1) T 0 0 0 0 1 1 1 0 1 1 1 0 Q(t) Q(t+1) S R 0 0 0 x 0 1 1 0 1 0 0 1 1 1 x 0...
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This note was uploaded on 01/27/2011 for the course CS 173 taught by Professor [email protected] during the Fall '08 term at University of Illinois at Urbana–Champaign.

  • Fall '08
  • [email protected]
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