Class Note for ECE 380 at UA-Digital Logic(11)
Class Note for ECE 380 at UA-Digital Logic(11)
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This 4 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Alabama - Tuscaloosa taught by a professor in Fall. Since its upload, it has received 13 views.
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Date Created: 02/06/15
ECE380 Digital Logic Introduction to Logic Circuits Variables functions truth tables gates and networks Logic circuits 0 Logic circuits perform operations on digital signals s Implemented as X Yi electron c circuits where X2 a Yz signal values are x3 ir3 restricted to a few h discrete values 5 quot tc 39quot9 Network 0 In binary logic circuits there are only two values 0 and 1 Xm Yn o The general form ofa logic circuit is a switching network discrete values Elearlca r conouar anoinoonno Dr o J Jackson La urezl easinca AcumvmaEnglneerlng Dr o J Jaclson La urezz Boolean algebra 0 Direct application to switching networks Work with Zstate devices 9 Zvalued Boolean algebra switching algebra Use a Boolean variable X Y etc to represent an input or output of a switching network Variable may take on only two values 0 1 X0 X1 These symbols are not binary numbers they simply represent the 2 states of a Boolean variable They are notvoltage levels although they commonly refer to the low or high voltage inputoutput of some circuit element Variables and functions Elearlca r conouar anoinoonno Dr o J Jackson LedureZCl o The simplest binary element is a switch that has two states 0 If the switch is controlled by X we say the switch is open if X 0 and closed if X 1 X n xi a Two states or a swtcn X p Symbol tor a swtcn easinca AcumvmaEnglneerlng Dr o J Jaclson LedureZA Variables and functions 0 Assume the switch controls a lightbulb as shown 7 The output is defined as the state of the light L lfthe lightis on sgt L1 lfthe light is offagt LO o The state of L as function ofx is s Lxgtlt o Lgtlt is a logic function 0 x is an input Variable m Battery X Light a Simple connection to a battery Power I supply p Usan a ground connection as the return path Variables and functions AND Elearlca r conouar anoinoonno Dr o J Jackson LedureZ 0 Consider the possibility of two switches controlling the state of the light 0 Using a series connection the light will be on only if both switches are closed LX11 X2 X1 X2 L1iffifand only if x1 AND xoare 1 AND operator Power X2 szz Supply I The circuit implements a log cal AN D functon The logical AND runction series connection easinca AcumvmaEnglneerlng Dr o J Jaclson LedureZS Variables and functions 0R 0 Using a parallel connection the light will be on only if either or both switches are closed Lgtlt1 X2 x1 x2 L1ifgtlt1 OR x2 is 1 or both Fuwer quot 0R operamr supply 1 Mg XI The Circuit implements The luglcal OR funttlurl parallel tunnettlun a log39cal 0R funcmn zlaonca sconomanznolnoanno Dr D J Jackson LeciureZT Variables and functions 0 Various seriesparallel connections would realize various logic functions Lgtlt1 X2 X3 X1 X2 39 X3 Power Supply 1 Eemrlca sconomaznonoanno Dr D J Jaclson LeciureZE Variables and functions o What would the following logic function look like if implemented via switches Lgtlt1 X2 X3 X4 X1 X2 0939 X4 Power Supply 1 zlaonca sconomanznolnoanno Dr D J Jackson LeciureZS Inversion 0 Before actions occur when a switch is closed What about the possibility of an action occurring when a switch is opened Lgtlt Where L1ifgtlt0 and L0 if x1 o Lgtlt is the inverse or complement of X gtltgtlt NOTgtlt The circuit implements a log cal NOT func on Eemrlca sconomaznonoanno Dr D J Jaclson LeciureZ 1D Inversion of a function o If a function is defined as X1 X2 X1 39 X2 0 Then the complement of f is 7gtlt1 X2gtlt1Tgtlt2 X1 X2 0 Similarily if fgtlt1 X2 X139 X2 0 Then the complement of f is 7gtlt1 X2 X139 gtlt2gtlt139 X2 zlaonca sconomanznolnoanno Dr D J Jackson Lecturele Truth tables o Tabular listing that fully describes a logic function Output value for all input combinations valuations X1 X1 X1 0 0 1 0 1 0 1 NOT 1 Eemrlca sconomaznonoanno Dr D J Jaclson LeciureZ 12 Truth tables Truth tables of functions Truth table for AND and OR functions of three variables m 1392 25 ml mtg r23 21 i 52 i 25 U U U U U 0 0 LL 0 LL U i U U EL 0 1 LL 0 LL 1 H U U H l 0 LL 0 LL I I U D II 1 L H H H If Lxyzxyz then the truth table for L yz 0 0 0 1 0 0 0 1 Electricl a cannula Englneenng m n J helmquot Lajurez 12 Electricl a cannula Engme mg m n J Jcksnn Lamquot 2 Jo Logic gates and networks Logic gates and networks Each basic logic operation AND OR NOT can be implemented resulting in a circuit element called a logic gate A logic gate has one or more inputs and one output that is a function of its inputs X1 X2 X1 X X1 X2 X1 X2 X71 2 Xn AND gates X1 X2 X1gtlt2 I x1gtlt2 mquot Xquot OR gates x gto NOT gate Electricl a cannula Englneenng m n J helmquot Lajurez 15 Electricl a cannula Engme mg m n J Jcksnn Lamquot 2 15 Logic gates and networks Logic gates and networks A larger circuit is implemented by a network of gates Called a logic network or logic circuit Draw the truth table and the logic circuit for the following function Fabc acbc u o b 0 0 1 1 0 0 1 1 40400000 04000400 Electricl a cannula Englneenng m n J helmquot Lajurez 11 Electricl a cannula Engme mg m n J Jcksnn Lamquot 2 1n Analysis of a logic network c To determine the functional behavior of a logic network we can apply all possible input signals to it EIgtEIgt1gt1 Xi Netwurkthat implementi 39xpx1 x2 sigma AcumvmerEngineying Dr D J Jackson La urezia Analysis of a logic network o The function of a logic network can also be described by a timing diagram gives dynamic behavior of the network 1 l n l l ll A l l E l i n l l l m Timing mamam r sewing AEomDmaEngmesring Dr D J New La urezm
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