Transcription of Chapter 2: Boolean Algebra and Logic Gates
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Chapter 2: Boolean Algebra and Logic Gates
1cs309 cs309 G. W. Cox Spring 2010 The University Of Alabama in Huntsville Computer ScienceThe University Of Alabama in Huntsville Computer ScienceChapter 2: Boolean Algebra andLogic Gatescs309 cs309 G. W. Cox Spring 2010 The University Of Alabama in Huntsville Computer ScienceThe University Of Alabama in Huntsville Computer ScienceBoolean AlgebraThe algebraic system usually used to work with binary Logic expressionsPostulates:1. Closure:Any defined operation on (0, 1) gives (0,1)2. Identity:0 + x = x ; 1 x = x3. Commutative:x + y = y + x ; xy = yx4. Distributive:x (y + z) = xy + xz; x + (yz) = (x + y)(x + z)5. Def of Complement:x + x = 1;x x = 06. At least 2 elements (0 and 1)Precedence rule: (1) parentheses(2) NOT(3) AND(4) cs309 G. W. Cox Spring 2010 The University Of Alabama in Huntsville Computer ScienceThe University Of Alabama in Huntsville Computer ScienceThe Duality Principle A Boolean expression that is always true is still true if we exchange OR with AND and 0 with 1 Examples:x + x = 1so: xx = 0x + y = y + xso: xy = yxNote that we cannot use Duality to say thatx + y =1, so xy = 0 Why not?
• So finding a way to simplify expressions will pay off in terms of the circuits we design cs309 G. W. Cox – Spring 2010 The University Of Alabama in Hunt sville Computer Science A metric for use in simplifying expressions • Define a “literal” as …
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