Glitches and Hazards in Digital Circuits

Transcription

1 Glithes n Hzrs in Digitl Ciruits Glithes n Hzrs in Digitl Ciruits After moment you hnge your min John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 Glithes n Hzrs in Digitl Ciruits Hzrs Glithes n Hzrs A glith is fst spike usully unwnte. A hzr is iruit whih my proue glith. We will see this hppens if the propgtion elys re unlne. The Clssifition of Hzrs y the Glith They My Proue stti-zero hzr; signl is stti t zero, glith rises. stti-one hzr; signl is one, glith flls. ynmi hzr; signl is hnging, up or own John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 2

2 Glithes n Hzrs in Digitl Ciruits The Two Bsi Stti-Hzr Ciruits The Two Bsi Stti-Hzr Ciruits Bsi Stti-Zero Hzr Ciruit FIG. - Bsi stti- Any iruit with stti- hzr must reue to the equivlent iruit of FIG. -, if other vriles re set to pproprite onstnts. FIG. -2 An emee stti- hzr Stti-zero Hzr s Chrteristis Two prllel pths for. One inverte. Reonverge t n AND gte. Eplintion: An OR gte with input psses the other input like wire John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 3 Glithes n Hzrs in Digitl Ciruits The Two Bsi Stti-Hzr Ciruits Bsi Stti-One Hzr Ciruit FIG. -3 Bsi stti- hzr iruit Any iruit with stti- hzr must reue to the equivlent iruit of FIG. -3 t FIG. -4 An emee stti- hzr Stti-One Hzr s Chrteristis Two prllel pths for. One inverte. Reonverge t n OR gte. John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 4

3 Glithes n Hzrs in Digitl Ciruits The Two Bsi Dynmi-Hzr Ciruits The Two Bsi Dynmi-Hzr Ciruits Bsi Dynmi Hzr Ciruits A stti hzr with n etr gte for the stti level hnge. Three prllel pths, one ontining stti hzr. ely FIG. -5 The si ynmi hzr iruit with its imee stti- hzr. Three Prllel pths ely FIG. -6 The si ynmi hzr iruit with its imee stti- hzr. Note tht ynmi hzr lwys hs three prllel pths. John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 5 Glithes n Hzrs in Digitl Ciruits The Two Bsi Dynmi-Hzr Ciruits Aing Dely to Hzrs Aing ely n remove hzrs, if one hs goo ontrol of propgtion elys. The originl iruit with the ely in the inverter. FIG. -7 Bsi stti- hzr iruit from FIG. -3. Note the hzr ppers on the flling ege of. Aing n equl ely in the other pth removes the flling-ege glith. Aing too muh ely will mke the glith pper on the rising ege. FIG. -8 Aing ely, moves the glith from to. To kill the glith lne the elys etly, if you n! ely At the silion lyout level, one might lne elys losely enough to suppress the glith. With stnr ells n fiel-progrmmle rrys, lning is hrer. But see Summry Of Hzrs on pge 36. John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 6

4 Glithes n Hzrs in Digitl Ciruits Hzrs on Krnugh Mp Hzrs on Krnugh Mp Ajent ut nonoverlpping irles on the mp re hzrs. y FIG. -9 Mp of stti- hzr. On the Σ of Π mp, eh OR gte input is seprte irle. K-mp of y= K-mp of y= K-mp of y = + Stning on top of hill gives. Chnging hills uses glith s one rosses the vlley. The shows the hzr. = = An interprettion of the K-mp of y. John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 7 Glithes n Hzrs in Digitl Ciruits Hzrs on Krnugh Mp A Stti- Hzrs on Mp Σ of Π mps n only show stti- hzrs, not stti- or ynmi hzr. AB FIG. - AND gtes hve een e to B the hzr. A The hzr is still the inverter B B n the OR gte. A + B The hzr ppers only when A =, B =. A Then signl trvels right A through the ANDs. Msking Hzr. B A To msk stti- hzrs gte tht stys high ross the trnsition. This gte is logilly reunnt. AB FIG. - The eqution F = B + A B hs reunnt term AB e A F = B + A + AB B This fills the vlley etween terms B +A+AB B n A. AB A AB John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 8

5 Glithes n Hzrs in Digitl Ciruits DeMorgn s Generl Theorem (Review) DeMorgn s Generl Theorem (Review) Simple form of DeMorgn s Theorems A B = A +B A B = A +B D+E = D E D+E = D E The generl form F(A,B,C,... +,,) = F(A,B,C,...,,+,) ) Tke the ul of F i) Brket ll groups of ANDs ii) Chnge AND to OR n OR to AND Clen rkets ) Invert ll vriles F=[A B C+D (A B+C)] A F={[{A B C} +{D ({A B}+C)}] A} F DUAL = {[{A+B+C} {D+({A+B} C)}]+A} F DUAL ={A+B+C} {D+{A+B} C}+A F ={A+B+C} {D+{A+B} C}+A Emples F = A B C {A B C} F = {A+B+C} F = A B C + A B {A B C} + {A B } F= {A+B+C} {A+B } F = A B (C + A B) {A B} (C+{A B }) F = {A+B}+(C { A+B }) John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 9 Glithes n Hzrs in Digitl Ciruits Getting Π of Σ Mp from n Eqution Tke Π of Σ eqution F The Π of Σ mp is foun y. Apply generlize DeMorgn to F This gives formul for F. 2. Mp F on Krnugh mp This is Σ of Π whih is esy to mp. 3. Chnge this F mpintompof F: write in the irle squres, write in the unirle squres. This gives the Π of Σ mp for F. Getting Π of Σ Mp from n Eqution F=(+B) ( +A) F=(+B) ( +A) F DUAL =( B) + ( A) Ple rs over single letters F =( B) +( A) F = B + A Mp of F with s irle. AB Σ of Π Mp of F AB Π of Σ mp for F F =(+B) ( +A) John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4

6 Glithes n Hzrs in Digitl Ciruits Showing Stti- Hzrs Showing Stti- Hzrs Use Π of Σ Mp Π of Σ mps show stti- hzrs. FIG. -2 AB A A+ F=(+B) ( +A) B B+ Plot Π of Σ mp. F=(+B) ( +A) F =( B) +( A) Cirle F on mp for F. Cirle s, not s. Gps etween jent irles show stti- hzrs. If the irles overlp, there is no hzr, The irles hve to e jent, not orner-to-orner. John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 Glithes n Hzrs in Digitl Ciruits Stti- Hzr with Mp Wrp Aroun Stti- Hzr with Mp Wrp Aroun Π of Σ mps show only stti- hzrs, not stti- or ynmi hzrs D E D+ E+ D E E+ D+ hzr F = (D + )(E + ) FIG. -3 Get Π of Σ mp F = (D + )(E + ) F =(D )+(E ) Cirle s not s. Gps etween jent irles show stti- hzrs. Don t forget wrp roun Msking Stti- Hzr on Π of Σ Mp FIG. -4 D E D+E E+ D+E D D+ hzr E D+E E+ D+ F= (D + )(E + ) (D + E) To msk the stti- hzr: AND F with term whih stys ross the hzr. The hzr is,d,e =,, to,,. The term whih stys ross the gp is,d,e = -,,, or (D+E). D E D+E D+E John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 2

7 Glithes n Hzrs in Digitl Ciruits Alger n Hzrs. Alger n Hzrs. In hzrs, elys temporrily mke =. In lger with hzrs, tret n s seprte vriles. For work with hzrs, o not use: Complementing Reution Swp Consensus = += +y=+y ( +y)=y y +y=y ( +y)(+y)=y ( + y)( +z)=z+y y + z = ( + z)( +y) y + yz + z =y+z ( + y)(y + z)( + z) = (+y)( +z) For work with ynmi hzrs, voi the istriutive lw. (Ftoring) The istriutive lws n rete ynmi hzrs from stti hzrs, even mske one. They will not remove or rete stti hzrs. The Simplifition Lws re All Right y+= ( + y)= The Distriutive Lws (y+z)=y+z +yz=(+y)(+z) John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 3 Glithes n Hzrs in Digitl Ciruits Alger of Hzrs Alger of Hzrs The si forms for hzrs n their equtions. nre trete s seprte vriles. If iruit hs hzr, the eqution of the iruit will reue to one of these forms. FIG. -5 Stti- Dynmi + Stti- + Dynmi ( + ) An Emple Below, hzr in must reue to si hzr iruit when = or when =. Stti- hzr + No Hzr ( + ) FIG. -6 Ciruit eqution is + when = get + = + The hzr is epose FIG. -7 Ciruit eqution is ( + ) When =, get ( + ) = When =, get ( + ) = There re no hzr John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 4

8 Glithes n Hzrs in Digitl Ciruits Alger of Hzrs The Distriutive Lw n Hzrs The istriutive lws n hnge 2 prllel pths into 3, this my rete ynmi hzr from stti one. They n rete ynmi hzr from mske hzr ( FIG. -8 ottom). FIG. -8 The istriutive lw hnging stti hzrs to ynmi hzrs. ORIGINAL CIRCUIT CIRCUIT AFTER APPLYING DISTRIBUTIVE LAW II + ( + )( + ) Stti- hzr + = ( + )( + ) When = + ( + )( + ) = + Stti- hzr when = ; ( + )( + ) =( + ) Dynmi hzr when = Mske Hzr When = ( + ) = + ( + )= + =+ Dynmi hzr when = John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 5 Glithes n Hzrs in Digitl Ciruits Alger of Hzrs DeMorgn s Lw Does Not Chnge Hzrs FIG. -9 DeMorgn s Lw oes not hnge stti hzrs or ynmi hzrs, other thn possily inverting them. ORIGINAL CIRCUIT CIRCUIT AFTER APPLYING DEMORGAN S LAW Stti- hzr Stti- hzr inverte = stti- hzr DeMorgn + = + = Dynmi hzr DeMorgn form of ynmi hzr + = ( +) John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 6

9 Glithes n Hzrs in Digitl Ciruits Metho Loting Hzrs Algerilly This metho will fin ll hzrs stti-, stti-, n ynmi. The iruits o not nee to e Σ of Π or Π of Σ. F=(++)e + (e +) It will fin ll types of hzrs on one pss. Etensions n show how to msk them. Metho Step ) Remove onfusing etene overrs. using DeMorgn. Step 2) Fin whih vriles nnot hve hzrs. Step 3) Chek for hzrs in eh vrile. Selet one vrile for heking. mke other vriles or to ring out hzr.. (A + ) + C => A +(+C) 2. Nee oth n 3., +, + Selet for heking A +(B + C) Mke A=, B=, C= + ( + ) Stti- hzr + John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 7 Glithes n Hzrs in Digitl Ciruits Fin All The Hzrs In F. Emple Fin All The Hzrs In F. F Metho Step ) Remove onfusing etene overrs This is legl euse DeMorgn s lw oes not hnge hzrs John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 8

10 Glithes n Hzrs in Digitl Ciruits Step ) Remove onfusing etene overrs. DeMorgn s Lws in Grphil Form (Review) FIG. -2 Equivlent grphil forms for AND, OR, NAND n NOR. A B A B = C = A +B C A AND B AND C D E D+E = F = D E F D OR E OR F G H G H = K = G +H G K NAND H NAND K D E D+E = F = D E NOR F D E NOR F FIG. -2 Removing onfusing inversions. NOR NOR NOR i ) Selet lternte levels strting t output. ii) Trnsform gtes NOR iii) Cnel k-to-k inverting irles iv) Result F = ( + )( + ) + John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 9 Glithes n Hzrs in Digitl Ciruits Step ) Remove onfusing etene overrs. Step 2. Estimting whih vriles might hve hzrs. A hzr, hs two pths whih reonverge in n AND or OR gte. One pth must hve n even numer of inversions, n the other pth must hve n o numer. One nee only hek for hzrs in vriles whih hve suh pths. Cheking iruit for potentilly hzrous pths. FIG. -22 Remove internl inverting irles using DeMorgn s lws. F To see hzrous pths: Chek for reonvergent pths one of whih is inverting. Only vrile hs suh pth; only n hve hzrs. F To hek whih vriles n hve hzrs. Chek whih vriles hve n \ Only hs oth n terms. F=(+)( + ) + John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 2

11 Glithes n Hzrs in Digitl Ciruits Step 3. Loting Hzrs From the Ciruit Step 3. Loting Hzrs From the Ciruit Eqution A. Tke the iruit eqution. F=(+)( + ) + B. Note whih vriles o not hve oth n. In this se, n. => only nees to e heke. C. Sustitute s n s for the other vriles. Try to get forms like:, +, +, (+). ( + ) ( + ) + F Type of hzr. ( + ) (+) + Stti- ( + ) ( + ) + + Dynmi ( + ) ( +) + + Stti- ( + ) ( +) + ( + ) ( +) + ( + ) ( +) + + ( + ) ( +) + + ( + ) ( +) + Stti- hzr in when,, =,,, Dynmi hzr in when,, =,,, Stti- hzr in when,, =,,. John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 2 Glithes n Hzrs in Digitl Ciruits Sme Emple With More Orgniztion n Sme Emple With More Orgniztion n Less Writing Eqution. F=(+)( + ) + Note only n hve hzr. Selet to to e the vrile tht hnges. Sequentilly sustitute or for the other letters. A little thought shows must e, else + ==>no => no hzr Set = first. ( + )( + ) + ( + )( + )+ muste,orno. ( + )( + )+ = ( + )+ try = = ( + )+ = + muste = + = + Stti- for try = = ( + )+ = + mye = + = Stti- for or my e = + = + Dynmi for + +,,,. John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 22

12 Glithes n Hzrs in Digitl Ciruits Sme Emple With More Orgniztion n Emple: Fin ll the single-vrile hnge hzrs f=( + )( + e ) Note only or n hve hzrs. e ( +)( + e ) e ( +)( + e ) must e ( =),ornoor e ( + )( + e)=(+)(+e) e =orno =( + )( +e) e if is =( + )( +) = ( + ) Dynmi for ny e e if is =( + )( + e)= ()( + e) ifeis = ()() Stti- e try = =(+)( + e) = if = n e= =(+)( + ) = Stti- e try = =(+)( + e) e try = = + )( + e) No hzr e try = = ( + )( + e) No hzr ( + ) e e John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 23 Glithes n Hzrs in Digitl Ciruits Loting Hzrs; More Comple Emple Loting Hzrs; More Comple Emple Eqution. F =[(+)+ (+) ] Note whih vriles o not hve oth n. Here ll vriles nee further heking. Selet one letter to to e the vrile tht hnges. Sequentilly (one t time) sustitute or for the other letters. A little thought helps selet whih letter to mke (or ) first. [( + ) + ( +) ] [ ( +) +(+ )] muste,orf [ ( + ) +( + )] =[(+)+ ], must e, or no set = =[(+)+ ]= [ +] my e. = [ + ] = Stti- for or my e =[ + ] = Stti- for [ ( + ) +( +)] must e, or F [ ( + ) +( +)] =[ + ] must e or no [( + ] =[] Stti- for - This hzr is inepenent of. [ ( + ) +( +)] =, must e,, or F [ ( + ) +( + )] = [ ] There is no, hene no hzr [(+) +( +)] =, must e,, or F [(+) +( + )] = [ ] There is no, hene no hzr John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 24

13 Glithes n Hzrs in Digitl Ciruits Grph of the previous hzr serh F=[(+)+ (+) ] [(+)+ ] [ +] [ + ] [(+ ] [(+) + (+) ] = + [] + [] John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 25 Glithes n Hzrs in Digitl Ciruits Sum-of-Prout Ciruits Hve No Stti- Implementing Hzr Free Ciruits Sum-of-Prout Ciruits Hve No Stti- Hzrs Sum of prouts iruits lwys hve n eqution of the form F = Stti- hzrs re like. { + is stti-} To get in F s ove on must ple n s inputs to the sme AND gte. This is ignornt. Rule I: Eept for the gross relessness of inluing terms like, Σ of Π implementtions hve no stti- hzrs. John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 26

14 Glithes n Hzrs in Digitl Ciruits Sum-of-Prout Ciruits Hve No Dynmi Hzrs Σ of Π iruit hve equtions of the form F = Dynmi hzrs re of the form + or (+). In F, tryfiing, n t ny omintion of or. A ynmi hzr in, must hve term ontining. In F ove, one n only get ynmi hzr y using the ignornt term. Thus Rule II is: Eept for the gross relessness of inluing terms like, Σ of Π implementtions hve no ynmi hzrs. John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 27 Glithes n Hzrs in Digitl Ciruits Sum-of-Prout Ciruits Hve Only Esily Sum-of-Prout Ciruits Hve Only Esily Eliminte Stti- Hzrs Σ of Π iruits n still hve stti- hzrs They re esily foun n remove using: Krnugh mp, or lgerilly.. FIG. -23 Mp of funtion F=+ It is Σ of Π The hzrs must ll e stti-. Hzr when, =,. A term to msk the hzr. F=++ Isshownontheright. John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 28

15 Glithes n Hzrs in Digitl Ciruits Prout-of Sum Ciruits Hve No Stti- Prout-of Sum Ciruits Hve No Stti- Hzrs Π of Σ iruit equtions re of the form F = (++)(++)(+++)(...)(+++) Stti- hzrs re of the form +. To get + in F one must ple n s inputs to the sme OR gte. This is ignornt. Eept for the gross relessness of inluing terms like ++, Π of Σ implementtions hve no stti- hzrs. Prout-of Sum Ciruits Hve No Dynmi Hzrs Eept for the gross relessness of inluing terms like, Π of Σ implementtions hve no ynmi hzrs. Prout-of Sum Ciruits Hve Only Esily Eliminte Stti- Hzrs Π of Σ iruits n still hve stti- hzrs They re esily foun n remove using Π of Σ Krnugh mp John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 29 Glithes n Hzrs in Digitl Ciruits Prout-of Sum Ciruits Hve Only Esily Emple: Single-Vrile-Chnge Hzr-Free Ciruit From Mp A igitl funtion efine y mp; FIG. -24(left). Choose irling for the mp; see FIG. -24 (mile), inite the hzrs. F= + + Then irles whih over the rrows; FIG. -24(right). The hzr free eqution, on this finl mp, is - F= FIG. -24 Left) Emple to e implemente s hzr free iruit. Centre) A possile Σ of Π enirlement showing hzrs. Right) The mp with the hzrs overe. F= + + Sine it is Σ of Π, ll single-vrile hnge hzrs re remove F= John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 3

16 Glithes n Hzrs in Digitl Ciruits Two-vrile-hnge hzrs Hzrs With Multiple Input Chnges Two-vrile-hnge hzrs Two-vriles hnges, move two squres on the Krnugh mp. Some 2-hnge hzrs re mskle. (upper rrow in FIG. -25) Mny 2-vrile hzrs re not mskle. (lower rrow) l A AB B A B A B F FIG. -25 Strt t squre A,B, =,, (the til of the rrows) Chnge oth B n to move to squre A,B, =,, (the he of the rrows). If B hnges slightly efore, one trvels the upper route. The vlley etween A n B my glith. A msking term AB n over the vlley. It only removes the glith on the upper pth. B B A +B+B If hnges slightly efore B, one tkes the lower pth. This will lwys glith. It nnot e overe. Covering the offening hnges the funtion. John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 3 Glithes n Hzrs in Digitl Ciruits Multiple Vrile Chnge Hzrs re Plentiful When Are Hzrs Importnt? Multiple Vrile Chnge Hzrs re Plentiful Tke synhronous iruit Let 4 flip-flops hnge t one. 6 possile mp squres. Most pths will hve funtion hzrs The vst numer of glithes generte y multiple vrile hnges FIG. -26 CLK AB D A CD D A COMBINATIONAL C D B B LOGIC D D C C C D D C D D D GLITCH HEAVEN A few of the possile pths C for 4-vrile hnging With 2 vriles hnging one is very likely to hve hzrs. With more vriles hnging they re like wves in the oen. But very fst glithes will e sore insie gtes (inertil ely).. John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 32

17 Glithes n Hzrs in Digitl Ciruits Hzrs o not hurt synhronous iruits Hzrs o not hurt synhronous iruits In loke logi, flip-flops only respon to the inputs slightly efore the lok ege. See the irles on the wveforms elow. All vriles hnge shortly fter the lok ege. The lok yle is me long enough so the glithes ie out long efore the lok ege. FIG. -27 The flip-flops only respon in the irle region on the wveforms elow. A glith t ny other time will not influene stte of the mhine. The glithes ie out long efore the lok ege. The glithes hve no influene on the stte. INPUT CLOCK D C Q D 2 D C Q 2 slow D 3 D C Q 3 DINPUT CLOCK Q D 2 Q 2 D 3 Q 3 Glithes must ie out efore net lok ege John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 33 Glithes n Hzrs in Digitl Ciruits Hzrs Kill Asynhronous Ciruits Hzrs Kill Asynhronous Ciruits By synhronous iruits, we men ones with feek tht n lth signls. A glith my uses wrong vlue to e lthe. All hzrs must e eliminte, or proven hrmless. RESET SET Q Anlog simultion is use to prove it hrmless. SET RESET S R Q Emple: Pling n R-S Lth in Synhronous Ciruit FIG. -28 The Russin Roulette of igitl esign with unloke lthes. These glithes ie out n GLITCH HEAVEN o no hrm. CLK D A D C D B D C D C D C D D D C A B C D COMBINATIONAL LOGIC KILLER GLITCH S R D C D C Lth lthes from glith. B output gets fe k. John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 34

18 Glithes n Hzrs in Digitl Ciruits Outputs where hzrs re of onern Outputs where hzrs re of onern Some isplys re very sensitive to glithes. Light emitting-ioe isplys my show slight ghosts in im light. Cthoe-ry tue isplys will often show ny glithes on their input signls. Memories Memory hips re synhronous lthes, n re sensitive to glithes. Memory ontrol les must e glith free. Glithes in synhronous inputs to synhronous iruits Asynhronous inputs to synhronous iruits must e hzr free. An input glith on the lok ege, my e pture s vli input. CLK D A Q A CLK D A D Q A C D C FALSE SIGNAL John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 35 Glithes n Hzrs in Digitl Ciruits Summry Of Hzrs Summry Of Hzrs Single vrile hnge hzrs Cn e foun n ure. Multiple vrile hnge hzrs Cn e foun Are very plentiful Cnnot e ure in generl, they re prt of the logi. My e reule to single vrile hnge. Hzrs re not importnt in truly synhronous iruits Eept for power onsumption. Don t mention flse-pths. Hzrs re importnt in Asynhronous iruits. Lthes n flip-flops Pulse thers Deouners Memory interfe signls High spee isplys Bus Control John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 36

19 Glithes n Hzrs in Digitl Ciruits Loting Hzrs; Emple three Loting Hzrs; Emple three Eqution. F = y(e + ) + ( e + e) + e y Selet one letter, ll it, to to e the vrile tht hnges. Vriles whih o not hve oth forms, n, hve no hrs. If only one, set ll symols ANDing to. + e set,,e to,, or no If only one, set symols ANDing t, n ORing t. y(e + ) set,e,y to,, or no. If ll s hve ommon ftor, fi ftor t. ( + ) + y musteorno e y y(e + ) + ( e + e) + e y e y y(e + ) + ( e + e) + e y muste,orno ey y(e + ) + ( e + e) +e y =y e + e + e y no => no hzrs in e y y(e + ) + ( e + e) + e y,e,y must e,, or no. ( + ) + ( + ) + = + no => no hzrs in. e y y(e + ) + ( e + e) + e y e must e or no. y y( + ) + ( + ) + y = y + + y y must e, or no = + + no => No hzrs. e y y(e + ) +( e + e) + e y musteornoe e y y(e + ) + ( e + e) + e y =y e +e + e y y must e or no e e =e +e + e = e +e must e e = e + e Stti- for e e y y(e + ) + ( e + e) + e y,,e must e,, or no y. y y( + ) +( + ) + y =+ y no y => No hzrs in y. John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 37 Glithes n Hzrs in Digitl Ciruits Loting Hzrs; Emple three Grph of the previous hzr serh F = y(e + ) + ( e + e) + e y e no no y(e + ) + ( e) e no no no y( ) + + y + e y no no no no y e + e + ey e + e e y e + e no e no e no e y(e + ) + e + e y y e + e + e y y e no y no y no y no y John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 38

20 Glithes n Hzrs in Digitl Ciruits Emple 4 Emple 4 Eqution. f=( + )( + e ) Note only or n hve hzr. e ( +)( + e ) e ( +)( + e ) must e ( = ), or no or e ( + )( + e)=(+)(+e) e =orno =( + )( +e) e if is =( + )( +) = ( + ) Dynmi for ny e e if is =( +)( +e)= ()( +e) if e is = ()() Stti- e try = =(+)( + e) = if = n e= = + = Stti- e try = =(+)( + e) e try = = ( + )( + e) No hzr e try = = ( + )( + e) No hzr e ( + ) e= or e John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 39 Glithes n Hzrs in Digitl Ciruits Emple 4. Prolem ) Ple rrows on the K-mp for F to show where ll the single-vrile-hnge stti- hzrs might our. ) On nother mp show wht AND terms must e e to F to msk these hzrs. Write the eqution for the simplest F you n fin tht still hs mske hzrs. You my hnge the originl four terms of F if it woul e enefiil. F= Prolem Given G= + + () Stte with resons, ut without oing ny lultion or mp work,: i) How mny stti- hzrs G hs. ii) How mny ynmi hzrs G hs. () Fin ll the single-vrile-hnge hzrs lgerilly. John Knight Eletronis Deprtment, Crleton University Printe; Mrh 24, 4 Moifie; Mrh 24, 4 4