Chapter2 - EE2006 Digital Design/S Ranganath II. Boolean...

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EE2006 Digital Design/S Ranganath II - 1 II. Boolean Algebra – Review Review material Fundamental Boolean operations. Deriving logic expressions from truth tables. ± SOP and POS expressions. ± Rules for deriving SOP and POS expressions. Boolean Identities. Simplifying logic expressions using Boolean identities. Karnaugh maps. ± Obtaining MSOP’s and MPOS’s ( new ) from K-maps. ± Don’t care conditions ( new ).
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EE2006 Digital Design/S Ranganath II - 2 Boolean algebra is the basic math used in digital circuits and computers. A Boolean variable takes on only 2 values: {0,1} , {T,F}, {Yes, No}, etc. There are 3 fundamental Boolean operations: AND OR NOT Z = A · B Z = AB Z = A+B Z = Ā Truth Table Truth Table Truth Table A truth table specifies output signal logic values for every possible combination of input signal logic values. In evaluating Boolean expressions, the Operation Hierarchy is: 1) NOT 2) AND 3) OR. Order can be superseded using ( … ). A B Z 0 0 0 1 1 0 1 1 0 0 0 1 A B Z 0 0 0 1 1 0 1 1 0 1 1 1 A Z 0 1 1 0
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EE2006 Digital Design/S Ranganath II - 3 Example: T D T C F B T A = = = = , , , What is the value of ) ( ) ( D B C B A Z + + = ? F D B C F D B C F F D B C F T Z = + = + + = + + = ) ( ) ( ) ( ) ( ) ( Deriving Logic Expressions From Truth Tables Truth Table: What is the Boolean expression for Z? Two equivalent logic expressions can be derived from Truth Tables: 1) Sum-of-Products (SOP) expressions: Several AND terms OR’d together, e.g. AB B A B A + + 2) Product-of-Sum (POS) expressions: Several OR terms AND’d together, e.g. ) )( ( B A B A + + Light must be ON when both switches A and B are OFF, or when both of them are ON. A B Z 0 0 0 1 1 0 1 1 1 0 0 1
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EE2006 Digital Design/S Ranganath II - 4 Rules for Deriving SOP Expressions 1) Find each row in TT for which output is 1 (rows 1 & 4) 2) For those rows write an AND term of all input variables.
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Chapter2 - EE2006 Digital Design/S Ranganath II. Boolean...

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