CompArch-Lec02-Combinational-Logic

CompArch-Lec02-Combinational-Logic - COSC3330 Computer...

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Lecture 2. Combinational Logic COSC3330 Computer Architecture Instructor: Weidong Shi (Larry), PhD Computer Science Department University of Houston
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Introduction A logic circuit is composed of s Inputs s Outputs s Functional specification Relationship between inputs and outputs s Timing specification Delay from inputs to outputs 5 inputs outputs functional spec timing spec
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Circuits Nodes s Inputs: A , B , C s Outputs: Y , Z s Internal: n1 Circuit elements s E1, E2, E3 6 A E1 E2 E3 B C n1 Y Z
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Types of Logic Circuits Combinational Logic s Outputs are determined by current values of inputs s Thus, it is memoryless Sequential Logic s Outputs are determined by previous and current values of inputs s Thus, it has memory 7 inputs outputs functional spec timing spec
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Rules of Combinational Composition A circuit is combinational if s Every node of the circuit is either designated as an input to the circuit or connects to exactly one output terminal of a circuit element s The circuit contains no cyclic paths Every path through the circuit visits each circuit node at most once s Every circuit element is itself combinational Select combinational logic? 8
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Boolean Equations The functional specification of a combination logic is usually expressed as a truth table or a Boolean equation s Truth table is in a tabular form s Boolean equation is in a algebraic form Example: S = F( A , B , C in ) out = F( , , in ) 9 Truth Table Boolean equation
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Terminology The complement of a variable A is A s A variable or its complement is called l iteral AND of one or more literals is called a product or implicant s Example: AB, ABC, B OR of one or more literals is called a sum s Example: A + B Order of operations s NOT has the highest precedence, followed by AND, then OR Example: Y = A + BC 10
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Minterms 11 A minterm is a product (AND) of literals involving all of the inputs to the function Each row in a truth table has a minterm that is true for that row (and only that row )
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Sum-of-Products (SOP) Form The function is formed by ORing the minterms for which the output is true s Thus, a sum (OR) of products (AND terms) All Boolean equations can be written in SOP form 12 A B Y 0 0 0 1 1 0 1 1 0 1 0 1 minterm A B A B A B A B Y = F(A, B) = AB + AB
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Boolean Algebra We learned how to write a boolean equation given a truth table s But, that expression does not necessarily lead to the simplest set of logic gates One way to simplify boolean equations is to use boolean algebra s Set of theorems s It is like regular algebra, but in some cases simpler
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This note was uploaded on 03/18/2011 for the course COSC 3330 taught by Professor Notknown during the Spring '11 term at University of Houston.

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CompArch-Lec02-Combinational-Logic - COSC3330 Computer...

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