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.
G. W. Cox – Spring 2010 The University Of Alabama in Hunt sville Computer Science SOP and Canonical SOP Form • A function is in Sum of Products (SOP) form if it is written as product terms ORed together – Example: f(x y z) = xy’z + xz + y • A function is in Canonical SOP form if it is in SOP form and all terms are minterms
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