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1ECET 331 – Digital Integrated CirciutsChapter 2Logic Functions and GatesECET 331 - Digital Integrated CircuitsBasic Logic Functionsz Three Basic Logic Functions• AND• OR• NOTz Other functions can be created from theseECET 331 - Digital Integrated CircuitsLogic Function Representationz Logic functions can be represented:• Algebraically• Using truth tables• Using electronic circuitsECET 331 - Digital Integrated CircuitsAlgebraic Representationz Uses Boolean algebraz Boolean variables have two states (binary)z Boolean operators include: • AND• OR• NOTECET 331 - Digital Integrated CircuitsTruth Table Representationz Defines the output of a function for every possible combination of inputsz A system with n inputs has 2npossible combinationsECET 331 - Digital Integrated CircuitsElectronic Circuit Representationz Uses logic gates to perform Boolean algebraic functionsz Gates can be represented by schematic symbolsz Symbols can be either distinctive-shape or rectangular-outline2ECET 331 - Digital Integrated CircuitsDistinctive Shape Schematic Symbolsz Uses different graphic representations for different logic functionsz Uses a bubble (a small circle) to indicate a logical inversionECET 331 - Digital Integrated CircuitsRectangular-Outline Schematic Symbolsz All functions are shown in rectangular form with the logic function indicated by standard notation inside the rectanglez The notation specifying the logic function is called the qualifying symbolz Inversion is indicated by a 1/2 arrowheadECET 331 - Digital Integrated CircuitsNOT Functionz One input and one outputz The output is the opposite logic level of the inputz The output is the complement of the inputECET 331 - Digital Integrated CircuitsNOT Function Boolean Representationz Inversion is indicated by a bar over the signal to be invertedY = AAY0110Truth TableECET 331 - Digital Integrated CircuitsNOT Function Electronic Circuitz Called a NOT gate or, more usually, an Inverterz Distinctive-shape symbol uses a triangle with inversion bubbleAY = AAY = AECET 331 - Digital Integrated CircuitsNOT Function Electronic Circuitz Rectangular symbol uses “1” and the inversion half arrowhead (IEEE std. 91-1984)AY = AAY = A113ECET 331 - Digital Integrated CircuitsAND Functionz Two or more inputs, one outputz Output is HIGH only when all of the inputs are HIGHz Output is LOW whenever any input is LOWz Logical ProductECET 331 - Digital Integrated CircuitsAND Boolean Representationz AND symbol is “•” or nothing at allY = A • BY = ABA B Y0 0 00 1 01 0 01 1 1Truth TableECET 331 - Digital Integrated CircuitsAND Function Electronic Circuitz Called an AND gatez Distinctive-shape symbol uses AND designationz Rectangular-shape symbol use “&” as designatorECET 331 - Digital Integrated CircuitsOR Functionz Two or more inputs, one outputz Output is HIGH whenever one or more input is HIGHz Output is LOW only when all of the inputs are LOWz Logical SumECET 331 - Digital Integrated CircuitsOR Boolean Representationz OR symbol is “+”z Y = A + BA B Y0 0 00 1 11 0 11 1 1Truth TableECET 331 - Digital Integrated CircuitsOR Function Electronic Circuitz Called an OR gatez Distinctive-shape symbol uses OR designationz Rectangular-shape symbol uses “≥”as designator4ECET 331 - Digital Integrated CircuitsActive Levelz The logic level defined as “ON” for a circuitz When a logic HIGH is “ON”, the signal is active-HIGHz When a logic LOW is “ON”, the signal is active-LOW• Indicated by a bubble at the output terminal of the logic functionECET 331 - Digital Integrated CircuitsNAND Functionz Generated by inverting the output of the AND functionz Output is HIGH whenever any input is LOWz Output is LOW only when all inputs are HIGHECET 331 - Digital Integrated CircuitsNAND Boolean Representationz Uses AND with an inversion overbarY = A•BY = ABA B Y0 0 10 1 11 0 11 1 0Truth TableECET 331 - Digital Integrated CircuitsNAND Function Electronic Circuitz Called a NAND gatez Uses the AND symbol with inversion on the outputECET 331 - Digital Integrated CircuitsNOR Functionz Generated by inverting the output of the OR functionz Output is HIGH only when all inputs are LOWz Outputs is LOW whenever any input is HIGHECET 331 - Digital Integrated CircuitsNOR Boolean Representationz Uses OR with an inversion overbarY = A + BA B Y0 0 10 1 01 0 01 1 0Truth Table5ECET 331 - Digital Integrated CircuitsNOR Function Electronic Circuitz Called a NOR gatez Uses OR symbol with inversion on the outputECET 331 - Digital Integrated CircuitsExclusive OR Gatez Two inputs, one outputz Output is HIGH when one, and only one, input is HIGHz Output is LOW when both inputs are equal – both HIGH or both LOWz Y = A B = AB + ABECET 331 - Digital Integrated CircuitsExclusive OR Gate Electronic Circuitz Called an XOR gateA B Y0 0 00 1 11 0 11 1 0Truth TableECET 331 - Digital Integrated CircuitsExclusive NOR Gatez Two inputs, one outputz Output is HIGH when both inputs are equal – both HIGH or both LOWz Output is LOW when one, and only one, input is HIGHECET 331 - Digital Integrated CircuitsExclusive NOR Gate Electronic Circuitz Called an XNOR gateA B Y0 0 10 1 01 0 01 1 1Truth TableECET 331 - Digital Integrated CircuitsGate Equivalence - NANDz A NAND gate can be represented by an AND gate with inverted outputz A NAND gate can be represented by an OR gate with inverted inputsY = AB6ECET 331 - Digital Integrated CircuitsGate Equivalence - NAND+ECET 331 - Digital Integrated CircuitsGate Equivalence - NORz A NOR gate can be represented by an OR gate with inverted outputz A NOR gate can be represented by an AND gate with inverted inputsz EXERCISEECET 331 - Digital Integrated CircuitsGate Equivalence – DeMorgan Formsz Change an AND function to an OR function and an OR function to an AND functionz Invert the inputsz Invert the outputsECET 331 - Digital Integrated CircuitsDeMorgan’s TheoremsA•B = A + BA + B = A•BECET 331 - Digital Integrated CircuitsLogic Switchesz Can be used to create logic voltages for circuit inputsz Provides a logic HIGH or LOW depending on switch positionz Commonly used switches include • normally-open pushbutton• normally-closed pushbutton• single-pole single-throw • single-pole double-throwECET 331 - Digital Integrated CircuitsLogic Switches7ECET 331 - Digital Integrated CircuitsLight Emitting Diodes (LEDs)z Conducts current in one direction and only illuminates when it is conductingz Can be


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WCU ECET 331 - Logic Functions and Gates

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