CompArch-Lec02-Combinational-Logic

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

This preview shows pages 1–14. Sign up to view the full content.

Lecture 2. Combinational Logic COSC3330 Computer Architecture Instructor: Weidong Shi (Larry), PhD Computer Science Department University of Houston

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Go To Forum
Choose a Forum

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Zoom-in a System Component
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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 )

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 56

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

This preview shows document pages 1 - 14. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online