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Berkeley ELENG 42 - Lecture Notes

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1Copyright 2003, Regents of University of CaliforniaLecture 10: 09//25/03 A.R. NeureutherVersion Date 09/14/03EECS 42 Intro. Digital Electronics Fall 2003EECS 42 Introduction to Digital ElectronicsAndrew R. NeureutherLecture # 10 Prof. King: Basic Digital Blocks•20 Min QuizBasic Circuit Analysis and Transients• Logic Functions, Truth Tables • Circuit Symbols, Logic from CircuitSchwarz and Oldham 11.1, 11.2 393-402Midterm 10/2: Lectures # 1-9: 4 Topics – See slide 2Length/Credit Review TBAhttp://inst.EECS.Berkeley.EDU/~ee42/Copyright 2003, Regents of University of CaliforniaLecture 10: 09//25/03 A.R. NeureutherVersion Date 09/14/03EECS 42 Intro. Digital Electronics Fall 2003First Midterm Exam: Topics• Basic Circuit Analysis (KVL, KCL)• Equivalent Circuits and Graphical Solutions for Nonlinear Loads• Transients in Single Capacitor Circuits• Node Analysis Technique and Checking SolutionsExam is in class 9:40-10:45 AM, Closed book, Closed notes, Bring a calculator, Paper providedCopyright 2003, Regents of University of CaliforniaLecture 10: 09//25/03 A.R. NeureutherVersion Date 09/14/03EECS 42 Intro. Digital Electronics Fall 2003Logic FunctionsLogic Statement: H = 1 if A and B and C are 1 or T is 1.We use “dot” to designate logical “and” and “+” to designate logical or in switching algebra. So how can we express this as a Boolean Expression?Logic Expression : To create logic values we will define “True” , as Boolean 1 and “False” , as Boolean 0. Boolean Expression: H = (A · B · C) + TExample: The logic variable H is true (H=1) if (A and B and C are 1) or T is true (logic 1), where all of A,B,C and T are also logical variables.Moreover we can associate a logic variable with a circuit node. Typically we associate logic 1 with a high voltage (e.g. 2V) and and logic 0 with a low voltage (e.g. 0V).Note that there is an order of operation, just as in math, and AND is performed before OR. Thus the parenthesis are not actually required here.Copyright 2003, Regents of University of CaliforniaLecture 10: 09//25/03 A.R. NeureutherVersion Date 09/14/03EECS 42 Intro. Digital Electronics Fall 2003Logical ExpressionsExample: Z = AExamples: X = A ·B ; Y = A ·B ·CExamples: W = A+B ; Z = A+B+CStandard logic notation :AND: “dot”OR : “+ sign”NOT: “bar over symbol for complement”With these basic operations we can construct any logical expression. Order of operation: NOT, AND, OR (note that negation of an expression is performed after the expression is evaluated, so there is an implied parenthesis, e.g. means .BA•B)(A•Copyright 2003, Regents of University of CaliforniaLecture 10: 09//25/03 A.R. NeureutherVersion Date 09/14/03EECS 42 Intro. Digital Electronics Fall 2003Logic Function Example• Boolean Expression: H = (A · B · C) + TThis can be read H=1 if (A and B and C are 1) or T is 1, orH is true if all of A,B,and C are true, or T is true, orThe voltage at node H will be high if the input voltages at nodes A, B and C are high or the input voltage at node T is highCopyright 2003, Regents of University of CaliforniaLecture 10: 09//25/03 A.R. NeureutherVersion Date 09/14/03EECS 42 Intro. Digital Electronics Fall 2003Logic Function Example 2Boolean Expression: B = A + S(D + T )This can be read B=1 if A = 1 or S=1 AND (D OR T =1), i.e.B=1 if {A = 1} or {S=1 AND (D OR T =1)}orB is true IF {A is true} OR {S is true AND D OR T is true}orThe voltage at node H will be high if {the input voltage at node A is high} OR {the input voltage at S is high and the voltages at D and T are high}You wish to express under which conditions your burglar alarm goes off (B=1):If the “Alarm Test” button is pressed (A=1) OR if the Alarm is Set (S=1) AND { the door is opened (D=1) OR the trunk is opened (T=1)}2Copyright 2003, Regents of University of CaliforniaLecture 10: 09//25/03 A.R. NeureutherVersion Date 09/14/03EECS 42 Intro. Digital Electronics Fall 2003Evaluation of Logical Expressions with “Truth Tables”Truth Table for Logic ExpressionABCTH00000100100011000100001111011100000101001110011101111101111111000001111000011111H = (A · B · C) + TCopyright 2003, Regents of University of CaliforniaLecture 10: 09//25/03 A.R. NeureutherVersion Date 09/14/03EECS 42 Intro. Digital Electronics Fall 2003Evaluation of Logical Expressions with “Truth Tables”The Truth Table completely describes a logic expressionIn fact, we will use the Truth Table as the fundamental meaning of a logic expression. Two logic expressions are equal if their truth tables are the sameCopyright 2003, Regents of University of CaliforniaLecture 10: 09//25/03 A.R. NeureutherVersion Date 09/14/03EECS 42 Intro. Digital Electronics Fall 2003The Important Logical FunctionsThe most frequent (i.e. important) logical functions are implemented as electronic “building blocks” or “gates”.We already know about AND , OR and NOT What are some others:Combination of above: inverted AND = NAND,inverted OR = NORAnd one other basic function is often used: the “EXCLUSIVE OR” … which logically is “or except not and”Copyright 2003, Regents of University of CaliforniaLecture 10: 09//25/03 A.R. NeureutherVersion Date 09/14/03EECS 42 Intro. Digital Electronics Fall 2003Some Important Logical Functions•“AND” •“OR”•“INVERT” or “NOT”•“not AND” = NAND•“not OR” = NOR•exclusive OR = XOR1BAh0(lBA)DCBA(or BAK++++BA BA i.e., differ) BA, when1(only BA⋅+⊕exceptC)BA(or BA⋅⋅⋅)0BA when1ly n(o BA==+)1 and when 0ly (o AB=BAn(or )Anot ACopyright 2003, Regents of University of CaliforniaLecture 10: 09//25/03 A.R. NeureutherVersion Date 09/14/03EECS 42 Intro. Digital Electronics Fall 2003These are circuits that accomplish a given logic function such as “OR”. We will shortly see how such circuits are constructed. Each of the basic logic gates has a unique symbol, and there are several additional logic gates that are regarded as important enough to have their own symbol. The set is: AND, OR, NOT, NAND, NOR, and EXCLUSIVE OR.Logic GatesABC=A·BANDC = ABNANDC = NORABNOTAORABC=A+BEXCLUSIVE ORABBAC ⊕=Copyright 2003, Regents of University of CaliforniaLecture 10: 09//25/03 A.R. NeureutherVersion Date 09/14/03EECS 42 Intro. Digital Electronics Fall 2003With a combination of logic gates we can construct any logic function. In these two examples we will find the truth


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Berkeley ELENG 42 - Lecture Notes

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