<- O tril -o cd21luqtu-mp03-y-https-ebookcentral-proquest-com.proxy.lirn.net/lib/univ-people-ebooks/reader.action?doclD=6226958&ppg = 195&c=UERG □ □ □ □ M [>8J CD kids CD Writing CD School CD FREE CD Timeline CD Church CD GTM *=} Amy@ € ^ G Frucci ^ S3 Q terrific.tools - Free... UoP ::: CCpics ca ProQuest Ebook Central™ Home Q Search lit Bookshelf ^ Profile (J) Language 0 Sign In ± © 0 © ft 6> P ! 0 D 1 ! cl Q, 0= Page 173 of 378 4 ► ■ • CHAPTER DIGITAL THEORY • — • ★ Q * In This Chapter • Using binary digits in electronics • Distinguishing between analog and digital electronics • Representing logical operations with truth tables • Using logic gates to control circuits Tin* idea of linking the binary digits ] and 0 to liigh-vokagc and low-collage levels, respectively made possible resolutionarv changes in Ikav we use electronics. ( n eat strides had already been made in elec-tnmics prior to this digital revolution. especially in the field of communications .md the launch of radio ami television. But once digital concepts wen1 overlaid on electronics theory. the pace of change in tcchm Jogy arcrleratcd to warp s|>ecd The Idea Behind Digital Concepts In 1937. a Massachusetts Institute of Technology* MIT' graduate stu-«l**nt named (.'Luule Shammu wrote "A Symbolic Analysis of Relay ami Switc hing Circuits.- which has l*een called the one of tin* most important masters theses of the century. In the pa|ier. Shannon pressed tlie use of Boolean algebras two-position analysis in creating digital circuits. The world of electronics w'.is from then on destined to change, even if it took a few decades for the idea to reach its lull |iotcntia). C (n) -o cd21luqtu-mp03-y-https-ebookcentral-proquest-com.proxy.lirn.net/lib/univ-people-ebooks/reader.action?doclD=6226958&ppg = 196&c=UERG □ □ □ □ M [>8J CD kids CD Writing CD School CD FREE CD Timeline CD Church CD GTM *=} Amy@ € f) G Frucci ^ S3 Q terrific.tools - Free... .Q UoP ::: CCpics ca ProQuest Ebook Central™ Home Q Search lit Bookshelf X Profile (J) Language 0 Sign In ± © 0 © ft 6> P | <t D 1 Q^Q^O^i Page 174 of 378 4 ► 174 • Btsic Euckchq. Third Edttion Titans of Electronics Claude Shannon < 1916-2001) is considered tin* father of digital circuits. hut his impact goes much further. Ilis work at Bdl 1 jIu .umI MIT with electronics, cryptography, and mathematics prodded ins|aratMNi to generations of future engineer* a quite a character. aitd often mventi-d oNitnaitiiMa fur |"«n* enjoyment: a uioton/ed page) stick, a rocket •immed flying chsk. and a nui-luiuc-al mouse tlul could solve a nww. He would rah’ las unkyrir through the lulls of Boll L«l» while jugging hub He and a fcDtM MIT professor enjoyed taking their matlM’iiutical re—nh im trips to I^s Vegas to test driv some theories at the Idackjack tai4e and rouk-tte wheel. I’nloituiuteK his filial wars w en1 spent in |Im> fog of Alzheimer s. hut I us lasting impact remains perfectly clear. Analog vs. Digital An analog signal is a continuous wave in both amplitude and in time. A digital signal is composed ol individual, identifiable steps. A wave in the ocean b an analog signal; the tick-tick-tick of the second hand on a dock b digital. The following figure shows a sine wave in analog form and digital form. The digital wave approximates the analog wave bv representing paints along the waveform. There are pros and cons to working with eac h signal hpe. Bec ause an analog waw b a continuous wave, it has more information. Homwr, be-* it has more information, it needs more processing and storage’ sjuce ncim 14.1 An, : i lop;, and iu tfigiul cquivjlcnt |boctom). C (n) -o cd21luqtu-mp03-y-https-ebookcentral-proquest-com.proxy.lirn.net/lib/univ-people-ebooks/reader.action?doclD=6226958&ppg = 197&c=UERG □ □ □ □ M [>8J CD kids CD Writing CD School CD FREE CD Timeline CD Church CD GTM *=} Amy@ € f) G Frucci ^ S3 Q terrific.tools - Free... .Q UoP ::: CCpics ca ProQuest Ebook Central™ Home Q Search lit Bookshelf X Profile (J) Language 0 Sign In ± © 0 © ft 6> P | <t D 1 Q^Q^O^i Page 175 of 378 4 ► • 175 A digital signal can Ik* much more compact than its analog counterpart, which means il requires fewer resources to transmit, receive, or store. A digital signal is also U*ss likelv to In* aTf«*cted In* noiar. In clwtronfci. noise is any unwanted interference with a signal. Noise sources can Ik* natural, due to the natui.il interact ion of electromagnetic fields, or man-made—from molors. fluorescent lights, radio or raiLir transmissions, wire less signals, and numerous other nans. One of the primary benefits of digital waves for electronics a that each discrete hit of information can he expressed numerically using Bou/ecin al-gfkra. Hu* states of "on" and "off or •high voltage" and 'low voltage' cun he represented by I or 0, which in turn can Ik* easily transmitted using svcitdies diodes, and tnuisistors in circuits. Boolean algebra is an approach to tlu* study of numbers that is based on !°gic. Logic is a branch ol philosophy that was developed In- tl»e ancient Greeks, including Aristotle. It starts with the bask* premise that an answer is either true or false. Aristotle projMised that there are laws of logic regarding a bi-valued reality in which statements are either true or false: X = X X * Y. not-X = Y. and X = not-Y. English mathematician George Boole expanded upon these classical views of logic and developed a system of algebra based on them. Boolean numbers are not the same as real numbers. Instead. Boolean nuni-Im*is represent a decision. They ask: Is it 1? If v«s 1. If no, 0. Each decision has the* possibility ol producing just two outcomes: I or 0. Truth T. Tlu* most common questions asked uIkiiiI a relationship of numbers in Boolean logic can Ik* expn-ssed bv the following logical ojMTations: ■ NOT: negation ■ AND: ccmjuiKfioii ■ OR: inclusion ■ NOR: neither/nor ■ NANI): not l»th 176 • Basic Eikikonks. Third Edition 10:08 PM 9/18/2025 <- O tril -o cd21luqtu-mp03-y-https-ebookcentral-proquest-com.proxy.lirn.net/lib/univ-people-ebooks/reader.action?doclD=6226958&ppg = 198&c=UERG □ □ □ □ M [>8J CD kids CD Writing CD School CD FREE CD Timeline CD Church CD GTM *=} Amy@ ^ ^ G Frucci ^ S3 Q terrific.tools - Free... -Q UoP ::: CCpics ca ProQuest Ebook Central™ Home Q Search lit Bookshelf X Profile (J) Language O Sign In ± © 0 © ft 6> P | 0 D 1 Q» Q, 0= | Page 176 of 378 4 ► a ■ • • ★ Q ♦. * 176 • Basic Euckchq. Third Edition ■ XOR: exclusive ■ XNOR: «'<|iulilv To represent dimconcrpU, wo can iuo something called 4 truth table. One value.called on operand, apes across |Ih* top of the tal4e IkxiaioIJK ami tin- tecimd o|mt.iimI goes down tin* tuble vertically For each question or logical ojx r.itHMi tin* various answers populate the Inn;. An operand is a quantity that has a matlieiuatical or logical operation e|H iWim «l on it. A truth table is used in Boolean logic to give the results for the |nssihle inputs and outputs The columns represent one side of the logical decision and tlie rows represent tlie other side of the logical decision. The result of each combination is depicted in the l«ox where the column and row intersect. In this table. 0 * I is true (because 0 is NOT equal to 1 >. wTiereas 0 * 0 is false. Let’s now represent tme with 1 and false with 0. as shown in the following figure. multiplication, division, or am* other real Instead, it the outputs of the question. “Is A not equal to The answer can Ik* true* or false, and we are using the binary digits 0 and I to represent both the o|ierands and the answers. This table does not n mat In-mat K.d operation. A F T T F 0 1 I nCUtll M-2 Airad-i uM for NOT <- O tril -o cd21luqtu-mp03-y-https-ebookcentral-proquest-com.proxy.lirn.net/lib/univ-people-ebooks/reader.action?doclD=6226958&ppg = 199&c=UERG □ □ □ □ M [>8J ^ CD kids CD Writing CD School CD FREE CD Timeline CD Church CD GTM *=} Amy@ ^ f) G Frucci ^ S3 Q terrific.tools - Free... UoP ::: CCpics ca ProQuest Ebook Central™ Home Q Search lit Bookshelf X Profile (J) Language 0 Sign In ± © 0 © ft 6> P ! 0 D 1 ! cl Q, 0= Page 177 of 378 4 ► a ■ • • ★ Q ♦. * D - Th(< ■ • 177 * 0 1 Truth tables can lx- treated for e*dl «l' tlie logical (Ijx ratiom «m just lewd Ia look at AND. The operation AND is troe only if both op-erands an- Inie—ill other words, only when botli ojx-rands an- I. Stated oiioIIm-t wav (he operand 0 n-|in-sents false and the operand I represents Inie. So false AND false is false; tme AND fain- is fain-: fain- AND tnu- is fain- but true AND tme is tnu-. I m V *■ <9 ^ do) $s> C (n) -o cd21luqtu-mp03-y-https-ebookcentral-proquest-com.proxy.lirn.net/lib/univ-people-ebooks/reader.action?doclD=6226958&ppg=200&c=UERG 178* Bask Euctromcs, Third Edition T»k- ojht.Ur)ii OR is false only if lx*tli operands are false—(hat b. only when Imtli ojierands are 0. The ofMTatHMi NOR b true only if l>ntli opr rands are false—only when both ojn-rands an- 0. TV iijM-ralmn NAND b tnie only if ul least one of its operands is false One njieraml must be 0 and one must he 1. Two common Derations of Boolean logic that we us*1 in electronics require two inputs XOR or 'eu lusive-OR” and XNOR or ’redurivn-NOR.* flN>se operations compare the two inputs and ask a question alaxit them. Here b the truth table for XOR. Looking at Use two inputs, tin- output is true if one (and only one) of the inputs is tnie. The XNOR gate is the inverse of XOR. For XNOR. looking at the two inputs, tlie output produces a value of true if and only if both operands are false or both operands are tnie. A 0 1 0 1 0 1 0 0 riGURf 14.4 Torfi uM fix NC* 0 1 0 1 1 1 1 0 f>CURf 14.7 Truh uW fix NAND □ □ □ □ M [>8J CD kids CD Writing CD School CD FREE CD Timeline CD Church CD GTM *=} Amy@ ^ f) G Frucci ^ S3 Q terrific.tools - Free... UoP ::: CCpics ca ProQuest Ebook Central™ Home Q Search lit Bookshelf ^ Profile (J) Language 0 Sign In ± © 0 © ft <?> P ! # D 1 ! cl Q, 0= Page 178 of 378 4 ► T-- • 179 <r □ □ □ □ -> C (ni -o cd21luqtu-mp03-y-https-ebookcentral-proquest-com.proxy.lirn.net/lib/univ-people-ebooks/reader.action?doclD=62269588fppg=2018tc=UERG M ^ C] k'ds CD Writing CD School CD FREE CD Timeline CD Church CD GTM Amy@ ^ G Frucci 0 S3 Q terrific.tools - Free... .Q UoP ::i CCpics ☆ / O US A © : ca ProQuest Ebook Central™ Home Q Search lit Bookshelf ^ Profile (J) Language 0 Sign In ± © Q © ft 6> P ! 0 D l ! o. Q, 0= Page 179 of 378 4 ► 0 0 1 a l l 0 f tCUHl 14.1 Tmh uMc for XOR 0 1 0 1 0 a 1 0 1 FIGURE 14.9 Tr.-tfi ubk forXNOR. logc. alter all— lint only if youmricdunkh 11 m ugh each > meiit. This is wit a problem for electronic' signals: tin v sinijdv do vlut th«ir circuit telLs I hem to do. When working with logM-.il statements, di'signer* uhI |)ngrunniers use trails such .is truth taides to kwp thi'ir turn .ml anus straight. Tlie fk’kl of logic takes some getting us«xl to. It all nukes sense—it is one ' Binary Numbers Binary numliers are distinct from Boolean i—liars. Binary muniN'rs use iIh> same two digits as Boolean numbers. but binary numliers are real numlx rs that represent values lievond 0 and I. (See Appendn C for details on mirk mg with binary numliers.1 A binary system can represent numbers from the base 10 system (our familiar numbering system with digits from 0 to 91 with a string of binary zeroes and ones. Binary' number representations 180 • Basic Euctronks. Third Edition of decimal numliers or binary-coded decimals (BCDs) can lie sent as indi-vm1u.i1 digits (in series) or as a group of hits (io parallel l. The usual arrangement is in ahylc. which is eight IhI*. A bit is a hitury digit. Four bits an1 cal ^ do) iW> <- O tril -o cd21luqtu-mp03-y-https-ebookcentral-proquest-com.proxy.lirn.net/lib/univ-people-ebooks/reader.action?doclD=6226958&ppg=201&c=UERG □ □ □ □ M [>8J CD kids CD Writing CD School CD FREE CD Timeline CD Church CD GTM *=} Amy® ^ ^ G Frucci ^ S3 Q terrific.tools - Free... UoP ::: CCpics ca ProQuest Ebook Central™ Home Q Search lit Bookshelf X Profile (J) Language 0 Sign In ± © 0 © ft 6> P ! 0 D 1 ! Q. Q, 0= Page 179 of 378 4 ► a ■ D - T~i • 179 0 0 1 i i 1 0 ftClUll ul Truth uMc fer XOR 0 1 0 1 0 3 l 0 1 A 0 1 FIGURE fOTwtfi able for XNOR. • • ★ Q ♦. * Tlic field iif logic (aid's some gelling used lo. Il all makes sense—it is g logic. after al—but only if vuu wort dclilx-raich through each state-mciit. Tbis is not a |iml>li>m for electronic signals: they simjrfs do what thair circuit tells them to do. When working with logical statements, ilcsigncrs .umI programmers uh> tixils such as truth lalik-s to krep thi'ir ones .mil won straight Binary Numbers Bman- numbers an> ilistinct from BiMilean 1—hen. Binary numbers use llw same two digits as Boolean niimben, but binary numliers are real numliers that represent values bevnnil 0 and I. (See Ap|iendn C for details on mirking with binarv numbers.) A binarv system can represent numliers from the luse 10 svstem (our familiar numbering svstem with digits from 0 to 91 with a string of binary zeroes and ones. Binary number representations <- O tril -o cd21luqtu-mp03-y-https-ebookcentral-proquest-com.proxy.lirn.net/lib/univ-people-ebooks/reader.action?doclD=6226958&ppg=202&c=UERG □ □ □ □ M [>8J CD kids CD Writing CD School CD FREE CD Timeline CD Church CD GTM *=} Amy@ € f) G Frucci ^ S3 Q terrific.tools - Free... .Q UoP ::: CCpics ca ProQuest Ebook Central™ Home Q Search lit Bookshelf ^ Profile (J) Language 0 Sign In ± © 0 © ft 6> P ! 0 D 1 ! cl Q, 0= Page 180 of 378 4 ► a ■ • • ★ Q ♦. < 180 • Basic Euctronks. Third Edition of dniinil numliers or binary-coded decimals (IK'I)s) can lx* sent as individual digits (in series) or as a group of bits (in parallel I. Tbe usual arrangement is in a/ryfr. which is eight Itits. &SI A bit is a Unary digit Four l>its an1 s ailed a liilible. A *«t of light Uts is a gainie Application to Electronics So why do >ou need to know al»ont binary' numU>rs ami Boolean operations? BeiaiiM* of the real-world application of these concepts to electronics. Yonv already teamed tliat. using diodes .uid transistors. you can cre.ite circuits that can |»ass thnmgli no (or relatively low-) voltage or relaliwlv higher-yuteage signals. If you go back to the idea of a computer as something that performs computations, you can see that creating a series of questions or logical operations coukl get you to a result. Of course, the number of operations required to periorm even simple tasks would require lots of these operations and. then 'fore, lots of circuits. I Logic Gates Each of the circuits that do these computations contains gates. In digital or logic circuits, the gates are called logic gatev. Each gate gives one output hut can haw multiple inputs. NANI) gates ami NOR gates an* known as untterml gale* because given enough combinations, they cun mimic the function of any oilier logic gate A NOT gale is also called an inierltr because it inverts ore signal into tin1 rexvrsc. When you begin designing your own circuits or doing x«nr own programming, you need to think like a circuit or a computer It is im|»rtant to map out the processes step l>y step. Designers and programmers often use llowchurts to represent the inputs and the decisi oiis .it each step. As you start mil in electronics. get in tlie habit of pLuming things out. You might lie going high-tech, but a pencil ami paper can still Ik* your most useful tools! ^ do) iW> □ □ □ □ M I>8J CD kids CD Writing CD School CD FREE CD Timeline CD Church CD GTM *=} Amy@ ^ f) G Frucci ^ S3 Q terrific.tools - Free... .Q UoP ::: CCpics ca ProQuest Ebook Central™ Home Q Search lit Bookshelf ^ Profile (J) Language 0 Sign In ± © Q © ft 6> P ! 0 D 1 ! cl Q, 0= Page 181 of 378 4 ► D jtm Tnioar -181 FtCUftf 14.19 Sfivboh fa van cun logic gain on a circiM board dagram Lab 14-1: AND Gate I To see how a digital logic gate works in action, let's construct an AND gale. Materials: 19V battery 2 single-pole, single-throw (SPST) switches Juniper wire I flashlight bulb Instructions: 1. Connect the Jumjier win's ns shown in the diagram to the two switches, tlie light bulb, and the batter)'. 2. Turn ini SWT to turn the light bulb ON. 3. Turn «i SW‘2 to turn the light hull) ON. Tile circuit is constructed so tliat if SWT - ON AND SW’2 > ON. then TIll'E. The tnu' answer is represented bv liigb voltage so it turns the light ON. 4. Now lets generate a FALSE output by turning off SWT. This yields a FALSE lor low voltage) because with SWT = OFF. it is not true that ^ do) iW> □ □ □ □ M I>8J CD kids CD Writing CD School CD FREE CD Timeline CD Church CD GTM Amy@ ^ ^ G Frucci ^ S3 Q terrific.tools - Free... .Q UoP ::: CCpics ca ProQuest Ebook Central™ Home Q, Search lit Bookshelf X Profile (J) Language 0 Sign In ± © Q © ft 6> P | <t D 1 Q^Q^O^i Page 182 of 378 4 ► a ■ • • ★ Q ♦. * 182 • Basic Euckchq. Third Edition ANO GJI» made wrth ivnlKhai SWI SW2 1 and 2 on N|M a on lOf 2oni«KrtolT LABftCUin III Aa AND jair both are on. The result would l>e the same if lioth were turned off. as thev both need to be ON to he TRUE. Lab 14-2: OR Gate Let's trv another gate, the OR (late. In this case, for the answer to be TRUE, either SW1 OR SW2 needs to lie ON. Use the same mateiiuls as in the* preceding lab. 1. Connect the Jumper wires as shown in tin- diagram to the two switches, the light hull, ami the Uittciv 2. Turn on SWI to turn tlie lamp ON. 3. Turn off SWI to turn the lamp OFF. Tilt' light Imlh will light because if we ask the .picstion SWI - ON OR SVV2 - OFF. the answer is TRUE 4. Tun. on SW2 to tun. tin- lamp OFF. 5. Tun. off SW2 to tun. the lamp ON. Again, the light bulb will light because if we ask the question SWI = OFF OR SW2 - ON. the answer is TRUE. <- O tril -o cd21luqtu-mp03-y-https-ebookcentral-proquest-com.proxy.lirn.net/lib/univ-people-ebooks/reader.action?doclD=6226958&ppg=205&c=UERG □ □ □ □ M [>8J CD kids CD Writing CD School CD FREE CD Timeline CD Church CD GTM *=} Amy@ ^ f) G Frucci ^ S3 Q terrific.tools - Free... UoP ::: CCpics ca ProQuest Ebook Central™ Home Q Search lit Bookshelf ± Profile (J) Language 0 Sign In ± © 0 © ft <?> P ! £ D 1 ! cl Q, 0= Page 183 of 378 4 ► a ■ • • ★ Q ♦. * i m # fti 6 ^ do) $s> □ □ □ □ M [>8J CD kids CD Writing CD School CD FREE CD Timeline CD Church CD GTM *=} Amy@ ^ ^ G Frucci ^ S3 Q terrific.tools - Free... .Q UoP ::: CCpics ca ProQuest Ebook Central™ Home Q Search lit Bookshelf ^ Profile (J) Language 0 Sign In ± © Q © ft 6> P ! 0 D 1 ! cl Q, 0= Page 184 of 378 4 ► a 184 • B-; c Eucuo-.ics. Third Ediion ■ Boolean alee lira is .ui expansion on classical logic tlicorv somposx-d of statements Jlial arc tme ill a I)i-valued world. The answers to each logical ipieslioii can bo depicted in truth tallies. ■ Using Boolean logic. you can create electronic circuits that can ja rlorm logical opr-rations Chapter Review Questions 1. Tin* Unary digits one ami zero are linked to wJtagc for one and for zero. 2. TnHv’Kalsc A simukI wave can only l>c represented In a digital wave. 3. Two lienefits of using digital signals mentioned in tin* text ani and Ghe tin* name of the logical operation that express the relationship lidow: I 4. Negation 5. Inclusion 6. Equality 7. Not both 8. Conjunction 9. Equality 10. Neither/ Nor