Overview of IEEE Standard

Transcription

1 Overview of IEEE tnr Explntion of Logi ymols emionutor Group DYZA

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3 Contents Title Pge. Introution ymol Composition ulifying ymols Generl ulifying ymols ulifying ymols for Inputs n Outputs ymols Insie the Outline Depeneny Nottion Generl Explntion G (AND) Depeneny Conventions for the Applition of Depeneny Nottion in Generl V (O) Depeneny N (Negte) (Exlusive-O) Depeneny Z (Interonnetion) Depeneny X (Trnsmission) Depeneny C (Control) Depeneny (et) n (eset) Depenenies EN (Enle) Depeneny M (Moe) Depeneny M Depeneny Affeting Inputs M Depeneny Affeting Outputs A (Aress) Depeneny Bistle Elements Coers Use of Coer to Proue Affeting Inputs Use of Binry Grouping to Proue Affeting Inputs equene of Input Lels equene of Output Lels List of Tles Tle Title Pge Generl ulifying ymols ulifying ymols for Inputs n Outputs ymols Insie the Outline ummry of Depeneny Nottion iii

4 List of Illustrtions Figure Title Pge ymol Composition Common-Control Blok Common-Output Element G Depeneny Between Inputs G Depeneny Between Outputs n Inputs G Depeneny With Dynmi Input Oe Affeting Inputs ustitution for Numers V (O) Depeneny N (Negte) (Exlusive-O) Depeneny Z (Interonnetion) Depeneny X (Trnsmission) Depeneny CMO Trnsmission Gte ymol n hemti Anlog Dt eletor (Multiplexer/Demultiplexer) C (Control) Depeneny (et) n (eset) Depenenies EN (Enle) Depeneny M (Moe) Depeneny Affeting Inputs Type of Output Determine y Moe An Output of the Common-Control Blok Determining n Output s Funtion Depenent eltionships Affete y Moe A (Aress) Depeneny Arry of 6 etions of Four Trnsprent Lthes With 3-tte Outputs Comprising 6-Wor 4-Bit nom-aess Memory Four Types of Bistle Ciruits Coer Generl ymol An X/Y Coe Converter An X/Otl Coe Converter Prouing Vrious Types of Depenenies Prouing One Type of Depeneny Use of the Binry Grouping ymol Input Lels Ftoring Input Lels Plement of 3-tte ymols Output Lels Ftoring Output Lels iv

5 Introution The Interntionl Eletrotehnil Commission (IEC) hs een eveloping very powerful symoli lnguge tht n show the reltionship of eh input of igitl logi iruit to eh output without showing expliitly the internl logi. At the hert of the system is epeneny nottion, whih will e expline in etion 4. The system ws introue in the UA in ruimentry form in IEEE/ANI tnr Y Lking t tht time omplete evelopment of epeneny nottion, it offere little more thn sustitution of retngulr shpes for the fmilir istintive shpes for representing the si funtions of AND, O, negtion, et. This is no longer the se. Interntionlly, Working Group of IEC Tehnil Committee TC-3 hs prepre new oument (Pulition 67-) tht onsolites the originl work strte in the mi 96s n pulishe in 97 (Pulition 7-5) n the menments n supplements tht hve followe. imilrly for the UA, IEEE Committee CC.9 hs revise the pulition IEEE t 9/ANI Y3.4. Now numere simply IEEE t 9-984, the IEEE stnr ontins ll of the IEC work tht hs een pprove, n lso smll mount of mteril still uner interntionl onsiertion. Texs Instruments is prtiipting in the work of oth orgniztions n this oument introues new logi symols in orne with the new stnrs. When hnges re me s the stnrs evelop, future eitions will tke those hnges into ount. The following explntion of the new symoli lnguge is neessrily rief n gretly onense from wht the stnrs pulitions will ontin. This is not intene to e suffiient for those people who will e eveloping symols for new evies. It is primrily intene to mke possile the unerstning of the symols use in vrious t ooks, n the omprison of the symols with logi igrms, funtionl lok igrms, n/or funtion tles will further help tht unerstning.

6 ymol Composition A symol omprises n outline or omintion of outlines together with one or more qulifying symols. The shpe of the symols is not signifint. As shown in Figure, generl qulifying symols re use to tell extly wht logil opertion is performe y the elements. Tle shows generl qulifying symols efine in the new stnrs. Input lines re ple on the left n output lines re ple on the right. When n exeption is me to tht onvention, the iretion of signl flow is inite y n rrow, s shown in Figure. Outline Generl ulifying ymol Input Lines * * * * * * * * Output Lines * Possile positions for qulifying symols relting to inputs n outputs Figure. ymol Composition All outputs of single, unsuivie element lwys hve ientil internl logi sttes etermine y the funtion of the element, exept when otherwise inite y n ssoite qulifying symol or lel insie the element. The outlines of elements my e utte or emee, in whih se the following onventions pply. There is no logi onnetion etween the elements when the line ommon to their outlines is in the iretion of signl flow. There is t lest one logi onnetion etween the elements when the line ommon to their outlines is perpeniulr to the iretion of signl flow. The numer of logi onnetions etween elements will e lrifie y the use of qulifying symols, n this is isusse further uner tht topi. If no initions re shown on either sie of the ommon line, it is ssume there is only one onnetion. When iruit hs one or more inputs tht re ommon to more thn one element of the iruit, the ommon-ontrol lok my e use. This is the only istintively shpe outline use in the IEC system. Figure shows tht, unless otherwise qulifie y epeneny nottion, n input to the ommon-ontrol lok is n input to eh of the elements elow the ommon-ontrol lok. Common-Control Blok Figure. Common-Control Blok

7 A ommon output epening on ll elements of the rry n e shown s the output of ommon-output element. Its istintive visul feture is the oule line t its top. In ition, the ommon-output element my hve other inputs s shown in Figure 3. The funtion of the ommon-output element must e shown y use of generl qulifying symol. Common-Output Element e f e f g Must, like other elements, hve qulifying symol to enote its logi funtion g Figure 3. Common-Output Element 3

8 3 ulifying ymols 3. Generl ulifying ymols Tle shows generl qulifying symols efine y IEEE tnr 9. These hrters re ple ner the top enter or the geometri enter of symol or symol element to efine the si funtion of the evie represente y the symol or of the element. Tle. Generl ulifying ymols YMBOL AND gte or funtion DECIPTION O gte or funtion. The symol ws hosen to inite tht t lest one tive input is neee to tivte the output. = Exlusive O. One n only one input must e tive to tivte the output. = Logi ientity. All inputs must stn t the sme stte. k An even numer of inputs must e tive. k + An o numer of inputs must e tive. The one input must e tive. or A uffer or element with more thn usul output pility. ymol is oriente in the iretion of signl flow. hmitt trigger; element with hysteresis X/Y Coer, oe onverter (DEC/BCD, BIN/OUT, BIN/7-EG, et.) MUX Multiplexer/t seletor DMUX or DX Demultiplexer Aer P utrter CPG Look-he rry genertor π Multiplier COMP Mgnitue omprtor ALU Arithmeti logi unit etriggerle monostle Nonretriggerle monostle (one shot) G Astle element. howing wveform is optionl.!g ynhronously strting stle G! Astle element tht stops with omplete pulse Gm hift register. m = numer of its CTm Counter. m = numer of its; yle length = m CT DIVm Counter with yle length = m CTm Asynhronous (ripple-rry) ounter; yle length = m OM e-only memory AM nom-ess re/write memory FIFO First-in, first-out memory I = Element powers up lere to stte I = Element powers up set to stte Φ Highly omplex funtion; gry-ox symol with limite etil shown uner speil rules Not ll of the generl qulifying symols hve een use in TI s t ooks, ut they re inlue here for ompleteness. 4

9 3. ulifying ymols for Inputs n Outputs ulifying symols for inputs n outputs re shown in Tle n re fmilir to most users, with the possile exeption of the logi polrity symol for iretly initing tive-low inputs n outputs (negtion). The oler logi negtion initor mens tht the externl stte proues the internl stte. The internl stte mens the tive stte. Logi negtion my e use in pure logi igrms; in orer to tie the externl n logi sttes to the levels high (H) n low (L), sttement of whether positive logi ( = H, = L) or negtive logi ( = L, = H) is eing use is require or must e ssume. Logi polrity initors eliminte the nee for lling out the logi onvention n re use in vrious t ooks in the symology for tul evies. The presene of the tringulr polrity initor inites tht the L logi level proues the internl stte (tive stte) or tht, in the se of n output, the internl stte proues the externl L level. Note how the tive iretion of trnsition for ynmi input is inite in positive logi, negtive logi, n with polrity inition. The internl onnetions etween logi elements utte together in symol my e inite y the symols shown in Tle. Eh logi onnetion my e shown y the presene of qulifying symols t one or oth sies of the ommon line n, if onfusion n rise out the numers of onnetions, use n e me of one of the internl onnetion symols. Tle. ulifying ymols for Inputs n Outputs YMBOL DECIPTION Logi negtion t input. Externl proues internl. Logi negtion t output. Internl proues externl. Ative-low input. Equivlent to in positive logi. Ative-low output. Equivlent to in positive logi. Ative-low input in the se of right-to-left signl flow Ative-low output in the se of right-to-left signl flow ignl flow from right to left. If not otherwise inite, signl flow is from left to right. Biiretionl signl flow Positive Logi Negtive Logi Polrity Inition Dynmi not use inputs H tive on not use not use L inite H trnsition L Nonlogi onnetion. A lel insie the symol usully efines the nture of this pin. Input for nlog signls (on igitl symol) (see Figure 4) # Input for igitl signls (on n nlog symol) (see Figure 4) Internl onnetion. stte on left proues stte on right. Negte internl onnetion. stte on left proues stte on right. Dynmi internl onnetion. Trnsition from to on left proues trnsitory stte on right. Internl input (virtul input). It lwys stns t its internl stte unless ffete y n overriing epeneny reltionship. Internl output (virtul output). Its effet on n internl input to whih it is onnete is inite y epeneny nottion. 5

10 The internl (virtul) input is n input originting somewhere else in the iruit n is not onnete iretly to terminl. The internl (virtul) output is likewise not onnete iretly to terminl. The pplition of internl inputs n outputs requires n unerstning of epeneny nottion, whih is expline in etion 4. In n rry of elements, if the sme generl qulifying symol n the sme qulifying symols ssoite with inputs n outputs woul pper insie eh of the elements of the rry, these qulifying symols usully re shown only in the first element. This is one to reue lutter n to sve time in reognition. imilrly, lrge ientil elements tht re suivie into smller elements my eh e represente y n unsuivie outline. 3.3 ymols Insie the Outline Tle 3 shows some symols use insie the outline. Note prtiulrly tht open-olletor (open-rin), open-emitter (open-soure), n 3-stte outputs hve istintive symols. An EN input ffets ll the externl outputs of the element in whih it is ple, plus the externl outputs of ny elements shown to e influene y tht element. It hs no effet on inputs. When n enle input ffets only ertin outputs, ffets outputs lote outsie the inite influene of the element in whih the enle input is ple, n/or ffets one or more inputs, form of epeneny nottion inites this (see 4.). The effets of the EN input on the vrious types of outputs re shown. It is prtiulrly importnt to note tht D input is lwys the t input of storge element. At its internl stte, the D input sets the storge element to its stte, n t its internl stte it resets the storge element to its stte. The inry grouping symol is expline more fully in etion 8. Binry-weighte inputs re rrnge in orer n the inry weights of the lest-signifint n the most-signifint lines re inite y numers. In this oument, weights of input n output lines re represente y powers of two, usully only when the inry grouping symol is use, otherwise, eiml numers re use. The groupe inputs generte n internl numer on whih mthemtil funtion n e performe or tht n e n ientifying numer for epeneny nottion (Figure 8). A frequent use is in resses for memories. everse in iretion, the inry grouping symol n e use with outputs. The onept is nlogous to tht for the inputs, n the weighte outputs inite the internl numer ssume to e evelope within the iruit. Other symols re use insie the outlines in orne with the IEC/IEEE stnrs, ut re not shown here. Generlly, these re ssoite with rithmeti opertions n re self-explntory. When nonstnrize informtion is shown insie n outline, it is usully enlose in squre rkets [ ]. The squre rkets re omitte when ssoite with nonlogi input, whih is inite y n X superimpose on the onnetion line outsie the symol. 6

11 Tle 3. ymols Insie the Outline YMBOL DECIPTION Postpone output (of pulse-triggere flip-flop). The output hnges when input inititing hnge (e.g., C input) returns to its initil externl stte or level (see etion 5). Bi-threshol input (input with hysteresis) N-P-N open-olletor or similr output tht n supply reltively low-impene L level when not turne off. equires externl pullup. Cple of positive-logi wire-and onnetion. + Pssive pullup output is similr to N-P-N open-olletor output ut is supplemente with uilt-in pssive pullup. N-P-N open-emitter or similr output tht n supply reltively low-impene H level when not turne off. equires externl pullown. Cple of positive-logi wire-o onnetion. + Pssive pullown output is similr to N-P-N open-emitter output ut is supplemente with uilt-in pssive pullown. 3-stte output Output with more thn usul output pility (symol is oriente in the iretion of signl flow) Enle input. When t its internl stte, ll outputs re enle. When t its internl stte, EN open-olletor n open-emitter outputs re off, 3-stte outputs re t normlly efine internl logi sttes n t externl high-impene stte, n ll other outputs (e.g., totem-poles) re t the internl stte. J, K,, Usul menings ssoite with flip-flops (e.g., = reset to, = reset to ) T Toggle input uses internl stte of output to hnge to its omplement. D Dt input to storge element equivlent to: m m hift right (left) inputs, m =,, 3, et. If m =, it usully is not shown. +m m Counting up (own) inputs, m =,, 3, et. If m =, it usully is not shown. m CT=5 CT=9 Binry grouping. m is highest power of. The ontents-setting input, when tive, uses the ontent of register to tke on the inite vlue. The ontent output is tive if the ontent of the register is s inite. Input line grouping... inites two or more terminls use to implement single logi input. Fixe-stte output lwys stns t its internl stte. X X E 7

12 4 Depeneny Nottion 4. Generl Explntion Depeneny nottion is the powerful tool tht sets the IEC symols prt from previous systems n mkes ompt, meningful symols possile. It provies the mens of enoting the reltionship etween inputs, outputs, or inputs n outputs without tully showing ll the elements n interonnetions involve. The informtion provie y epeneny nottion supplements tht provie y the qulifying symols for n element s funtion. In the onvention for the epeneny nottion, the terms ffeting n ffete re use. In ses where it is not evient whih inputs must e onsiere s eing the ffeting or the ffete ones (e.g., if they stn in n AND reltionship), the hoie my e me in ny onvenient wy. o fr, types of epeneny hve een efine n ll of these re use in vrious TI t ooks. X epeneny is use minly with CMO iruits. They re liste elow in the orer in whih they re presente n re summrize in Tle 4. ECTION DEPENDENCY TYPE O OTHE UBJECT 4. G, AND 4.3 Generl ules for Depeneny Nottion 4.4 V, O 4.5 N, Negte (Exlusive-O) 4.6 Z, Interonnetion 4.7 X, Trnsmission 4.8 C, Control 4.9, et n, eset 4. EN, Enle 4. M, Moe 4. A, Aress 8

13 4. G (AND) Depeneny A ommon reltionship etween two signls is to hve them ANDe together. This tritionlly hs een shown y expliitly rwing n AND gte with the signls onnete to the inputs of the gte. The 97 IEC pulition n the 973 IEEE/ANI stnr showe severl wys to represent this AND reltionship using epeneny nottion. While ten other forms of epeneny hve sine een efine, the wys to invoke AND epeneny re now reue to one. In Figure 4, input is ANDe with input n the omplement of is ANDe with. The letter G hs een hosen to inite AND reltionships n is ple t input, insie the symol. A numer onsiere pproprite y the symol esigner ( hs een use here) is ple fter the letter G n lso t eh ffete input. Note the r over the t input. G Figure 4. G Depeneny Between Inputs In Figure 5, output ffets input with n AND reltionship. The lower exmple shows tht it is the internl logi stte of unffete y the negtion sign tht is ANDe. Figure 6 shows input to e ANDe with ynmi input. G G Figure 5. G Depeneny Between Outputs n Inputs G Figure 6. G Depeneny With Dynmi Input The rules for G epeneny n e summrize thus: When Gm input or output (m is the numer) stns t its internl stte, ll inputs n outputs ffete y Gm stn t their normlly efine internl logi sttes. When the Gm input or output stns t its stte, ll inputs n outputs ffete y Gm stn t their internl sttes. 9

14 4.3 Conventions for the Applition of Depeneny Nottion in Generl The rules for pplying epeneny reltionships in generl follow the sme pttern s ws illustrte for G epeneny. Applition of epeneny nottion is omplishe y:. leling the input (or output) ffeting other inputs or outputs with the letter symol initing the reltionship involve (e.g., G for AND) followe y n ientifying numer, ppropritely hosen, n. leling eh input or output ffete y tht ffeting input (or output) with tht sme numer. If it is the omplement of the internl logi stte of the ffeting input or output tht oes the ffeting, then r is ple over the ientifying numers t the ffete inputs or outputs (Figure 4). If two ffeting inputs or outputs hve the sme letter n sme ientifying numer, they stn in n O reltionship to eh other (Figure 7). G G Figure 7. Oe Affeting Inputs If the ffete input or output requires lel to enote its funtion (e.g., D), this lel is prefixe y the ientifying numer of the ffeting input (Figure 5). If n input or output is ffete y more thn one ffeting input, the ientifying numers of eh of the ffeting inputs pper in the lel of the ffete one, seprte y omms. The norml reing orer of these numers is the sme s the sequene of the ffeting reltionships (Figure 5). If the lels enoting the funtions of ffete inputs or outputs must e numers (e.g., outputs of oer), the ientifying numers to e ssoite with oth ffeting inputs n ffete inputs or outputs re reple y nother hrter selete to voi miguity, e.g., Greek letters (Figure 8). α Gα α G Figure 8. ustitution for Numers

15 4.4 V (O) Depeneny The symol enoting O epeneny is the letter V (Figure 9). V V Figure 9. V (O) Depeneny When Vm input or output stns t its internl stte, ll inputs n outputs ffete y Vm stn t their internl sttes. When the Vm input or output stns t its internl stte, ll inputs n outputs ffete y Vm stn t their normlly efine internl logi sttes. 4.5 N (Negte) (Exlusive-O) Depeneny The symol enoting negte epeneny is the letter N (Figure ). N = If =, then =, if =, then = Figure. N (Negte) (Exlusive-O) Depeneny Eh input or output ffete y n Nm input or output stns in n exlusive-o reltionship with the Nm input or output. When n Nm input or output stns t its internl stte, the internl logi stte of eh input n eh output ffete y Nm is the omplement of wht it otherwise woul e. When n Nm input or output stns t its internl stte, ll inputs n outputs ffete y Nm stn t their normlly efine internl logi sttes.

16 4.6 Z (Interonnetion) Depeneny The symol enoting interonnetion epeneny is the letter Z. Interonnetion epeneny is use to inite the existene of internl logi onnetions etween inputs, outputs, internl inputs, n/or internl outputs. The internl logi stte of n input or output ffete y Zm input or output is the sme s the internl logi stte of the Zm input or output, unless moifie y itionl epeneny nottion (Figure ). Z where Z where Z G Z Figure. Z (Interonnetion) Depeneny

17 4.7 X (Trnsmission) Depeneny The symol enoting trnsmission epeneny is the letter X. Trnsmission epeneny is use to inite ontrolle iiretionl onnetions etween ffete input/output ports (Figure ). X / If =, there is iiretionl onnetion etween n. If =, there is iiretionl onnetion etween n. Figure. X (Trnsmission) Depeneny When n Xm input or output stns t its internl stte, ll I/O ports ffete y this Xm input or output re iiretionlly onnete n stn t the sme internl logi stte or nlog signl level. When n Xm input or output stns t its internl stte, the onnetion ssoite with this set of epeneny nottion oes not exist. Although the trnsmission pths represente y X epeneny re inherently iiretionl, use is not lwys me of this property. This is nlogous to piee of wire, tht my e onstrine to rry urrent in only one iretion. If this is the se in prtiulr pplition, then the iretionl rrows shown in Figures, 3, n 4 woul e omitte. n n p X Figure 3. CMO Trnsmission Gte ymol n hemti p # # MUXDMUX x ///3 3 3 Figure 4. Anlog Dt eletor (Multiplexer/Demultiplexer) 3

18 4.8 C (Control) Depeneny The symol enoting ontrol epeneny is the letter C. Control inputs typilly re use to enle or isle the t (D, J, K,, or ) inputs of storge elements. They my tke on their internl sttes (e tive) either sttilly or ynmilly. In the ltter se, the ynmi input symol is use s shown in the thir exmple of Figure 5. C D C C,D G C D Note AND reltionship of n G,D C,D,D G C Input selets whih of or is store when goes low. Figure 5. C (Control) Depeneny When Cm input or output stns t its internl stte, the inputs ffete y Cm hve their normlly efine effet on the funtion of the element, i.e., these inputs re enle. When Cm input or output stns t its internl stte, the inputs ffete y Cm re isle n hve no effet on the funtion of the element. 4

19 4.9 (et) n (eset) Depenenies The symol enoting set epeneny is the letter. The symol enoting reset epeneny is the letter. et n reset epenenies re use if it is neessry to speify the effet of the omintion = = on istle element. Cse in Figure 6 oes not use or epeneny. Cse NC? NC? Cse NC NC Cse 3 NC NC Cse 4 NC NC Cse 5 NC NC = externl stte, = externl stte, NC = no hnge,? = unspeifie Figure 6. (et) n (eset) Depenenies When n m input is t its internl stte, outputs ffete y the m input ret, regrless of the stte of n input, s they normlly woul ret to the omintion =, =. ee ses, 4, n 5 in Figure 6. When n m input is t its internl stte, outputs ffete y the m input ret, regrless of the stte of n input, s they normlly woul ret to the omintion =, =. ee ses 3, 4, n 5 in Figure 6. When n m or m input is t its internl stte, it hs no effet. Note tht the nonomplementry output ptterns in ses 4 n 5 re only pseuo stle. The simultneous return of the inputs to = = proues n unforeseele stle n omplementry output pttern. 5

20 4. EN (Enle) Depeneny The symol enoting enle epeneny is the omintion of letters EN. The ENm input hs the sme effet on outputs s n EN input, see 3., ut it ffets only those outputs lele with the ientifying numer m. It lso ffets those inputs lele with the ientifying numer m. By ontrst, n EN input ffets ll outputs n no inputs. The effet of n ENm input on n ffete input is ientil to tht of Cm input (Figure 7). EN EN Figure 7. EN (Enle) Depeneny When n ENm input stns t its internl stte, the inputs ffete y ENm hve their normlly efine effet on the funtion of the element n the outputs ffete y this input stn t their normlly efine internl logi sttes, i.e., these inputs n outputs re enle. When n ENm input stns t its internl stte, the inputs ffete y ENm re isle n hve no effet on the funtion of the element, n the outputs ffete y ENm re lso isle. Open-olletor outputs re turne off, 3-stte outputs stn t their normlly efine internl logi sttes ut externlly exhiit high impene, n ll other outputs (e.g., totem-pole outputs) stn t their internl sttes. 6

21 4. M (Moe) Depeneny The symol enoting moe epeneny is the letter M. Moe epeneny is use to inite tht the effets of prtiulr inputs n outputs of n element epen on the moe in whih the element is operting. If n input or output hs the sme effet in ifferent moes of opertion, the ientifying numers of the relevnt ffeting Mm inputs will pper in the lel of tht ffete input or output etween prentheses n seprte y solii (Figure ). 4.. M Depeneny Affeting Inputs M epeneny ffets inputs the sme s C epeneny. When n Mm input or Mm output stns t its internl stte, the inputs ffete y this Mm input or Mm output hve their normlly efine effet on the funtion of the element, i.e., the inputs re enle. When n Mm input or Mm output stns t its internl stte, the inputs ffete y this Mm input or output hve no effet on the funtion of the element. When n ffete input hs severl sets of lels seprte y solii (e.g., C4/ /3+), ny set in whih the ientifying numer of the Mm input or Mm output ppers hs no effet n is to e ignore. This represents isling of some of the funtions of multifuntion input. The iruit in Figure 8 hs two inputs, n, tht ontrol whih one of four moes (,,, or 3) will exist t ny time. Inputs, e, n f re D inputs sujet to ynmi ontrol (loking) y the input. The numers n re in the series hosen to inite the moes so inputs e n f re only enle in moe (for prllel loing) n input is only enle in moe (for seril loing). Note tht input hs three funtions. It is the lok for entering t. In moe, it uses right shifting of t, whih mens shift wy from the ontrol lok. In moe 3, it uses the ontents of the register to e inremente y one ount. e f C4/ /3+ M 3,4D,4D,4D Note tht ll opertions re synhronous. In moe ( =, = ), the outputs remin t their existing sttes s none of the inputs hs n effet. In moe ( =, = ), prllel loing tkes ple through inputs e n f. In moe ( =, = ), shifting own n seril loing through input tke ple. In moe 3 ( = = ), ounting up y inrement of one per lok pulse tkes ple. Figure 8. M (Moe) Depeneny Affeting Inputs 4.. M Depeneny Affeting Outputs When n Mm input or output stns t its internl stte, the ffete outputs stn t their normlly efine internl logi sttes, i.e., the outputs re enle. When n Mm input or output stns t its internl stte, t eh ffete output ny set of lels ontining the ientifying numer of the Mm input or Mm output hs no effet n is to e ignore. When n output hs severl ifferent sets of lels seprte y solii (e.g.,,4/3,5), only those sets in whih the ientifying numer of this Mm input or Mm output ppers re to e ignore. Figure 9 shows symol for evie whose output n ehve like either 3-stte output or n open-olletor output, epening on the signl pplie to input. Moe exists when input stns t its internl stte n, in tht se, the 3-stte symol pplies n the open-element symol hs no effet. When =, moe oes not exist, so the 3-stte symol hs no effet n the open-element symol pplies. 7

22 M EN / Figure 9. Type of Output Determine y Moe In Figure, if input stns t its internl stte, estlishing moe, output stns t its internl stte only when the ontent of the register equls 9. ine output is lote in the ommon-ontrol lok with no efine funtion outsie of moe, the stte of this output outsie of moe is not efine y the symol. M CT=9 Figure. An Output of the Common-Control Blok In Figure, if input stns t its internl stte, estlishing moe, output stns t its internl stte only when the ontent of the register equls 5. If input stns t its internl stte, output stns t its internl stte only when the ontent of the register equls. M CT=5 CT= Figure. Determining n Output s Funtion In Figure, inputs n re inry weighte to generte the numers,,, or 3. This etermines whih one of the four moes exists. M 3 N4 G5 (/3)4,4,4/3,5 e f g Figure. Depenent eltionships Affete y Moe At output e, the lel set using negtion (if = ) is effetive only in moes n 3. In moes n, this output stns t its normlly efine stte s if it h no lels. At output f, the lel set hs effet when the moe is not, so output e is negte (if = ) in moes,, n 3. In moe, the lel set hs no effet, so the output stns t its normlly efine stte. In this exmple,,4 is equivlent to (//3)4. At output g there re two lel sets. The first set, using negtion (if = ), is effetive only in moe. The seon set, sujeting g to AND epeneny on, hs effet only in moe 3. Note tht in moe none of the epeneny reltionships hs ny effet on the outputs, so e, f, n g stn t the sme stte. 8

23 4. A (Aress) Depeneny The symol enoting ress epeneny is the letter A. Aress epeneny provies ler representtion of those elements, prtiulrly memories, tht use ress ontrol inputs to selet speifie setions of multiimensionl rrys. uh setion of memory rry usully is lle wor. The purpose of ress epeneny is to llow symoli presenttion of the entire rry. An input of the rry shown t prtiulr element of this generl setion is ommon to the orresponing elements of ll selete setions of the rry. An output of the rry shown t prtiulr element of this generl setion is the result of the O funtion of the outputs of the orresponing elements of selete setions. Inputs tht re not ffete y ny ffeting ress input hve their normlly efine effet on ll setions of the rry, wheres, inputs ffete y n ress input hve their normlly efine effet only on the setion selete y tht ress input. An ffeting ress input is lele with the letter A, followe y n ientifying numer tht orrespons with the ress of the prtiulr setion of the rry selete y this input. Within the generl setion presente y the symol, inputs n outputs ffete y n Am input re lele with the letter A, whih stns for the ientifying numers, i.e., the resses of the prtiulr setions. Figure 3 shows 3-wor y -it memory hving seprte ress line for eh wor, n uses EN epeneny to explin the opertion. To selet wor, input is tken to its stte, whih estlishes moe. Dt n now e loke in the inputs mrke,4d. Unless wors n 3 re lso selete, t nnot e loke in t the inputs mrke,4d n 3,4D. The outputs will e the O funtions of the selete outputs, i.e., only those enle y the tive EN funtions. EN EN A EN3 A A3 C4 e C4,4D,4D f e g A,4D A f h g 3,4D 3,4D h,4d 3,4D 3 Figure 3. A (Aress) Depeneny The ientifying numers of ffeting ress inputs orrespon with the resses of the setions selete y these inputs. They nee not neessrily iffer from those of other ffeting epeneny inputs (e.g., G, V, N,...) euse in the generl setion presente y the symol they re reple y the letter A. If there re severl sets of ffeting Am inputs for the purpose of inepenent n possily simultneous ess to setions of the rry, then the letter A is moifie to A, A, et. Beuse they hve ess to the sme setions of the rry, these sets of A inputs my hve the sme ientifying numers. Figure 4 is nother illustrtion of the onept. 9

24 AM 6 4 EN A 5 3 C A,D A Figure 4. Arry of 6 etions of Four Trnsprent Lthes With 3-tte Outputs Comprising 6-Wor 4-Bit nom-aess Memory TYPE OF DEPENDENCY Tle 4. ummry of Depeneny Nottion LETTE YMBOL AFFECTING INPUT AT IT TATE AFFECTING INPUT AT IT TATE Aress A Permits tion (ress selete) Prevents tion (ress not selete) Control C Permits tion Prevents tion Enle EN Permits tion Prevents tion of inputs outputs off outputs t externl high impene, no hnge in internl logi stte. Other outputs t internl stte. AND G Permits tion Imposes stte Moe M Permits tion (moe selete) Prevents tion (moe not selete) Negte (Exlusive-O) N Complements stte No effet eset Affete output rets s it woul to =, = No effet et Affete output rets s it woul to =, = No effet O V Imposes stte Permits tion Trnsmission X Biiretionl onnetion exists Biiretionl onnetion oes not exist Interonnetion Z Imposes stte Imposes stte These letter symols pper t the ffeting input (or output) n re followe y numer. Eh input (or output) ffete y tht input is lele with tht sme numer. When the lels EN,, n pper t inputs without the following numers, the esriptions ove o not pply. The tion of these inputs is esrie uner etion 3.3.

25 5 Bistle Elements The ynmi input symol, the postpone output symol, n epeneny nottion provie the tools to ifferentite four min types of istle elements n mke synhronous n synhronous inputs esily reognizle (Figure 5). The first olumn shows the essentil istinguishing fetures; the other olumns show exmples. Trnsprent Lthes Cm D C C D Ege Triggere Cm D C J C K Pulse Triggere J Cm C C K Dt Lokout Cm J C K J C K Figure 5. Four Types of Bistle Ciruits

26 Trnsprent lthes hve level-operte ontrol input. The D input is tive s long s the C input is t its internl stte. The outputs respon immeitely. Ege-triggere elements ept t from D, J, K,, or inputs on the tive trnsition of C. Pulse-triggere elements require the setup of t efore the strt of the ontrol pulse; the C input is onsiere stti sine the t must e mintine s long s C is t its stte. The output is postpone until C returns to its stte. The t lok-out element is similr to the pulse-triggere version exept tht the C input is onsiere ynmi, in tht shortly fter C goes through its tive trnsition, the t inputs re isle n t oes not hve to e hel. However, the output is still postpone until the C input returns to its initil externl level. Notie tht synhronous inputs n e reily reognize y their epeneny lels (D, J, K,, ) ompre to the synhronous inputs (, ), whih re not epenent on the C inputs.

27 6 Coers The generl symol for oer or oe onverter is shown in Figure 6. X n Y my e reple y pproprite initions of the oe use to represent the informtion t the inputs n t the outputs, respetively. X/Y Figure 6. Coer Generl ymol Inition of oe onversion is se on the following rule: Depening on the input oe, the internl logi sttes of the inputs etermine n internl vlue. This vlue is reproue y the internl logi sttes of the outputs, epening on the output oe. The inition of the reltionships etween the internl logi sttes of the inputs n the internl vlue is omplishe y:. leling the inputs with numers. In this se the internl vlue equls the sum of the weights ssoite with those inputs tht stn t their internl stte, or y. repling X y n pproprite inition of the input oe n leling the inputs with hrters tht refer to this oe. The reltionships etween the internl vlue n the internl logi sttes of the outputs re inite y:. leling eh output with list of numers representing those internl vlues tht le to the internl stte of tht output. These numers shll e seprte y solii, s shown in Figure 7. This leling my lso e pplie when Y is reple y letter enoting type of epeneny (see etion 7). If ontinuous rnge of internl vlues proues the internl stte of n output, this n e inite y two numers tht re inlusively the eginning n the en of the rnge, with these two numers seprte y three ots (e.g., = 4/5/6/7/8/9) or y. repling Y y n pproprite inition of the output oe n leling the outputs with hrters tht refer to this oe, s shown in Figure 8. Alterntively, the generl symol my e use, together with n pproprite referene to tle, in whih the reltionship etween the inputs n outputs is inite. This is reommene wy to symolize POM fter it hs een progrmme. FUNCTION TABLE INPUT OUTPUT 4 X/Y /4 /3 3/4 7 e f g g f e Figure 7. An X/Y Coe Converter 3

28 4 X/OCT 4 e f 3 g 4 FUNCTION TABLE INPUT g f e h 5 i 6 j 7 OUTPUT j i h Figure 8. An X/Otl Coe Converter

29 7 Use of Coer to Proue Affeting Inputs It often ours tht set of ffeting inputs for epeneny nottion is proue y eoing the signls on ertin inputs to n element. In suh se, use n e me of the symol for oer s n emee symol (Figure 9). X/Y /3 G G V4 N5 C3 Figure 9. Prouing Vrious Types of Depenenies If ll ffeting inputs proue y oer re of the sme type n their ientifying numers re shown t the outputs of the oer, Y (in the qulifying symol X/Y) my e reple y the letter enoting the type of epeneny. The initions of the ffeting inputs shoul then e omitte (Figure 3). X/M X/Y M M M Figure 3. Prouing One Type of Depeneny 5

30 8 Use of Binry Grouping to Proue Affeting Inputs If ll ffeting inputs proue y oer re of the sme type n hve onseutive ientifying numers not neessrily orresponing with the numers tht woul hve een shown t the outputs of the oer, use n e me of the inry grouping symol. k externl lines effetively generte k internl inputs. The rket is followe y the letter enoting the type of epeneny, followe y m/m. The m is to e reple y the smllest ientifying numer n the m y the lrgest one, s shown in Figure 3. X/Y A A A A A3 A4 A5 6 A6 7 A7 G 5 8 X/Y 3 G5 G6 G7 G8 Figure 3. Use of the Binry Grouping ymol 6

31 9 equene of Input Lels If n input hving single funtionl effet is ffete y other inputs, the qulifying symol (if there is ny) for tht funtionl effet is preee y the lels orresponing to the ffeting inputs. The left-to-right orer of these preeing lels is the orer in whih the effets or moifitions must e pplie. The ffete input hs no funtionl effet on the element if the logi stte of ny one of the ffeting inputs, onsiere seprtely, woul use the ffete input to hve no effet, regrless of the logi sttes of other ffeting inputs. If n input hs severl ifferent funtionl effets or hs severl ifferent sets of ffeting inputs, epening on the moe of tion, the input my e shown s often s require. However, there re ses in whih this metho of presenttion is not vntgeous. In those ses the input my e shown one with the ifferent sets of lels seprte y solii (Figure 3). No mening is tthe to the orer of these sets of lels. If one of the funtionl effets of n input is tht of n unlele input to the element, solius preees the first set of lels shown. M G /, M G, G /C C /G G Figure 3. Input Lels If ll inputs of omintionl element re isle (use to hve no effet on the funtion of the element), the internl logi sttes of the outputs of the element re not speifie y the symol. If ll inputs of sequentil element re isle, the ontent of this element is not hnge n the outputs remin t their existing internl logi sttes. Lels my e ftore using lgeri tehniques (Figure 33). (/)D D/D,,3,4(5+/6 ),,3,4,5+/,,3,4,6 Figure 33. Ftoring Input Lels 7

32 equene of Output Lels If n output hs numer of ifferent lels, regrless of whether they re ientifying numers of ffeting inputs or outputs or not, these lels re shown in the following orer:. If the postpone output symol hs to e shown, this omes first, if neessry, preee y the initions of the inputs to whih it must e pplie. Followe y the lels initing moifitions of the internl logi stte of the output, suh tht the left-to-right orer of these lels orrespons with the orer in whih their effets must e pplie 3. Followe y the lel initing the effet of the output on inputs n other outputs of the element. ymols for open iruit or 3-stte outputs, where pplile, re ple just insie the outsie ounry of the symol, jent to the output line (Figure 34). G EN,, Figure 34. Plement of 3-tte ymols If n output nees severl ifferent sets of lels tht represent lterntive funtions (e.g., epening on the moe of tion), these sets my e shown on ifferent output lines tht must e onnete outsie the outline. However, there re ses in whih this metho of presenttion is not vntgeous. In those ses, the output my e shown one, with the ifferent sets of lels seprte y solii (Figure 35). M CT=9/CT=5 M CT=9 CT=5 M CT=9/CT=5 M CT=9 CT=5 Figure 35. Output Lels Two jent ientifying numers of ffeting inputs in set of lels tht re not lrey seprte y nonnumeri hrter shoul e seprte y omm. If set of lels of n output not ontining solius ontins the ientifying numer of n ffeting Mm input stning t its internl stte, this set of lels hs no effet on tht output. Lels my e ftore using lgeri tehniques (Figure 36). (/)3,3/,3,,3,4(5CT=9/5CT=),,3,4,5CT=9/,,3,4,5CT= Figure 36. Ftoring Output Lels 8