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Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 3 Boolean Operations and Expressions AdditionAddition 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 1 MultiplicationMultiplication 0 * 0 = 0 0 * 1 = 0 1 * 0 = 0 1 * 1 = 1

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 5 Laws Boolean Algebra Laws Boolean Algebra Commutative LawsCommutative Laws Associative LawsAssociative Laws Distributive LawDistributive Law

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 7 Laws of Boolean Algebra Commutative Law of Multiplication:Commutative Law of Multiplication: A * B = B * A

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 8 Laws of Boolean Algebra Laws of Boolean Algebra Associative Law of Addition:Associative Law of Addition: A + (B + C) = (A + B) + C

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 9 Laws of Boolean Algebra Laws of Boolean Algebra Associative Law of Multiplication:Associative Law of Multiplication: A * (B * C) = (A * B) * C

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 10 Laws of Boolean Algebra Laws of Boolean Algebra Distributive Law:Distributive Law: A(B + C) = AB + AC

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 21 Rules of Boolean Algebra Rule 10: A + AB = ARule 10: A + AB = A AND Truth TableOR Truth Table

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 23 Rules of Boolean Algebra Rule 12: (A + B)(A + C) = A + BCRule 12: (A + B)(A + C) = A + BC AND Truth TableOR Truth Table

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 25 DeMorgans Theorems Theorem 1Theorem 1 Theorem 2Theorem 2 Remember: Break the bar, change the sign

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 27 Standard Forms of Boolean Expressions The sum-of-product (SOP) formThe sum-of-product (SOP) form Example: X = AB + CD + EF The product of sum (POS) formThe product of sum (POS) form Example: X = (A + B)(C + D)(E + F)

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 34 VHDL VHDL Entity StructureEntity StructureExample: entity AND_Gate1 is port(A,B:in bit:X:out bit); end entity AND_Gate1

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 35 VHDL VHDL ArchitectureArchitectureExample: architecture LogicFunction of AND_Gate1 is begin X<=A and B; end architecture LogicFunction

Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Slide 36 Hardware Description Languages (HDL) Hardware Description Languages (HDL) Boolean Expressions in VHDLBoolean Expressions in VHDL ANDX <= A and B; ORX <= A or B; NOTX <= A not B; NANDX <= A nand B; NORX <= A nor B; XORX <= A xor B; XNORX <= A xnor B;