Exam Review. John Knight Electronics Department, Carleton University March 2, 2009 ELEC 2607 A MIDTERM

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1 riting Exms: Exm Review riting Exms += riting Exms synhronous iruits Res, yles n Stte ssignment Synhronous iruits Stte-Grph onstrution n Smll Prolems lso Multiple Outputs, n Hrer omintionl Prolem riting Exms: riting Exms EE 2607 MIDTERM rleton University Mrh 4, 2008 Open ook. In the spirit of the oe of honor of rleton University I solemnly elre this exmintion is ompletely my own work, n I i not i my nswer to ny question y ishonorle mens. NME STUDENT No rite nswers on the question sheet. Use itionl pper if neessry. ttempt ll questions. UTHORIED MEMORND TURN OFF ell phones n personl ommunitions equipment n EVE THEM IN OUR KNPSK. Notes, ooks, n non-ommuniting lultor re llowe. oolen If you use mp, inite in the spe unerneth it, for whih funtion it is. If you use lger, inite the rules use t the right sie of eh line. Espeilly for sorption, D2, Swp, onesus n other less ovious ones Mrks will e eute if you on t! ) Simplify g= +DEF + PEH +JK +MNG D D mp of 2

2 riting Exms: riting Exms riting Exms Timing yourself: 80 min, 00% 5 min for 0%. /2 hour for lenup. Give Up: If you n t get it move on. RTF: Re The Foolish uestion; re it gin DMN IT ht ws ske for? Just the stte tle? Then on t mke K-mps. Di it wnt iruit. Then rw it! Exm Rey + = ook for simple methos: Don t o ll lger questions y multiplying out. (++)(++)(+)= += NO NO NO! F oes not equl its ul F = (++)(++)(+) F ul = ++(+) = +++ = + (F ul ) ul = F = (+)(+) Tke ul Dist +nythng = (use simp twie) + = + 3 riting Exms: riting Exms Time yourself: 5 min for 0%. /2 hour for lenup. Give Up: Try n esier question. RTF: Re it gin riting Exms ook for simple methos: Don t o ll lger questions y multiplying out. (++)(++)(+)= First look for simplifitions. re there three m spe for the nswer? Do you nee thirty? No! see simplifition elow. + = = + Simplify t eh step: Right elow: +nything = eft leg: +nything = + nything Nose: += F n F ul F = (++)(++)(+) F ul = ++(+) = +++ = + (F ul ) ul = F = (+)(+) Tke ul Dist +nythng = (use simp twie) + =

3 ommon Mistkes: ommon Mistkes ommon Mistkes. Sying is the sme s 2. Sying n expression is equl to its ul. 3. Not using + = to simplify expressions efore using omplex rules. Not reuing using + E = + E. Simplifying n reuing first sves lger. 4. Sying + = Everyoy knows etter thn this, ut they still o it. 5. hen you tke ul, or generl Demorgn, o not put in the rkets in your he. ( + ) + DE ==> (+)(D +E) ( + ) + DE ==> (() + ) + (DE) ==> ((+))(D +E) 6. Not knowing D2. + =( + )( +) 7. Krnugh mp my not give the simplest iruit, ut it oes give the simplest Σ of Π iruit. Unless you mess up the loops 5 oolen lger: oolen lger oolen lger. Simplify ( + ) 2. Simplify D +E 3. Tke the ul of F=( + )( + ) + 4. Ftor + 5. Ftor + 6. Fin the ul of G=( + )( + ) + D 7. Ftor + D 8. onstrut simplest iruit with MUs + D + D 6

4 oolen lger: oolen lger. Simplify ( + ) 2. Simplify D +E 3. Tke the ul of F=( + )( + ) + 4. Ftor + 5. Ftor + oolen lger rule += rule DeMorg + D + E =+D+E rule +E=+E F={( + )( + )} + rket NDs F ul ={()+()} ( + )( + ) rule D2 ( +)( + ) rule D2 =( + )( +)( + ) rule D2 6. Fin the ul of G=( + )( + ) + D {( + )( + )} + D rket NDs G ul ={(0)+()}D ul 0 =D rules 0=0; x+0=x 7. Ftor + D ( + )( + D) rule D2 8. onstrut with MUs + D + D =( + )( + )( + D)( + D) rule D2 + D D + D = =D 7 oolen lger: oolen lger K-Mps; ommon Errors hek our Mp Entries One vrile in the wrong squre, you re tost! hek for rp roun, n ier rp roun Using lger fter mp simplifition. Usully not help: K-mp gives the simplest Σ of Π iruit. it of ftoring might lower gte ount. Poor Poor ou fin two etter loops three gtes Goo Fin iggest loops + = ( + ) two gtes Don t Tret Multiple Output Prolems ike Unrelte iruits Mp of F Mp of G SHRE GTES Mp of F 2 gtes, none shre 9 gtes, 3 shre Mp of G 8

5 oolen lger: oolen lger K-Mps; ommon Errors Do not onfuse 5-vrile mps n ul-output mps. 5-vrile use the lrgest irles, Try to enlrge irle y using oth mps. Multiple output Shring is very importnt to sve gtes Often (esp exms) some smller irles will give fewer gtes. shring lowers gte ount. smller irles inrese letter ount. lne these Multiple Output Mpping Rules Do Hlf-Mps First (Exept for Ps) No frien rule ll friens gone to rk sie rule st two rules re heuristis They help, ut ut not lwys, They o not reple ll thinking. 9 Multiple Outputs Detils: Multiple Outputs Detils Multiple Outputs Detils Exmple.-33 Fin the equtions with minimum logi Minimiztion with shring () Hlf Mps ook for hlf-mp irles (one letter terms) These o not require n ND gte. n n e irle without loss of potentil gte shring. No Friens (one )Rule (2) irle squres tht re on only one mp thus nnot e shre. No Friens, They ent To The Drk Sie, Rule (2) Fin squres tht nnot e usefully shre euse tht squre on other mps is lrey irle. irle them hlf-mp qurter-mp one Mp f No frien one frien ie Mp g 0

6 Multiple Outputs Detils: Multiple Outputs Detils No est Friens Rule onesome rule) (2) oop squres tht pper on only one mp There is no wy to shre them. oop them with s mny rothers, or s, s possile. No est friens Just rothers irle him with his rothers est irle y (fmily) No frien 00 here 0 0 Mp of Mp of No frien here No frien here Mp of Mp of Multiple Outputs Detils: Multiple Outputs Detils My est Friens re Gone Rule. (They went over to the rk sie) (2) ith no est friens left, we nnot usefully shre loops. oop these new frienless s with fmily. h one est frien Frien went to the rk sie Mp of oop him with fmily Mp of est frien s gone est frien s gone Mp of oop him His est frien is gone. Mp of 2

7 Multiple Outputs Detils: Multiple Outputs Detils Exmp.-33Fin the minimum Σ of Π Minimum numer of ND terms Poor Metho etter Metho () irle hlf mps (none) rgest irles 7 ND terms (2) No Friens, ( s on only one mp) F F G G H H oop Frienless s, they will never shre Unfortuntely you hve hoies; severl wys to loop some squres hoies F F G H hoies G H 3 Fin the minimum Σ of Π(ont): Fin the minimum Σ of Π(ont) Fin the minimum Σ of Π(ont) hoies hoie () hosen irles re she Shows unneessry reunny hoie (2) hoie (3) hoies John s Solution 6 ND terms Tom s Solution 5 ND terms nie s Solution 5 ND terms F F F 4 G G G F G H H H H

8 Prolems from De 96.: Prolems from De 96. Sketh the Output veforms D Prolems from De 96. D th (inverte lok) Trnsprent when? the when? D D Flip-Flop ege triggere Equilivlent to gte D G D th Trnsprent when the when 5 Prolems from De 96.: thes et from De 96. Exmple.-34 Sketh the Output veforms D T T T Prolems from De 96. D th (inverte lok) Trnsprent when low the when high D D Flip-Flop Rising ege triggere D G T T T NOR gte D th Trnsprent when = the when =0 6

9 Prolems from De 96.: Prolems from De 96. thes et from De 96.thes et from De 96. Exmple.-35 Sketh the Output veforms D T T T D th (inverte lok) Trnsprent when lok low the when high D D Flip-Flop Rising ege triggere D G T T T NOR gte D th Trnsprent when = the when=0 7 Prolems from De 96.: thes et. from De 96. Exmple.-36 Sketh the Output veforms R S E R S Prolems from De 96. Reset() - set() th Set output to 0 when R=0 Set output = when RS=0 Store output when SR= F Synhronous Stte Grph x=0 x=0 x= 0 z=0 x= z= K Stte= Synhronous Stte Grph G x= x=0 z= x= x=0/z= x=/z=0 K Stte Show stte s well s Stte Stte 8

10 Prolems from De 96.: thes et. from De 96. Exmple.-37 Sketh the Output veforms R S E R() S() Prolems from De 96. Reset()-set() th Set output = when RS=0 Set output to 0 when R=0 Store output when SR= Set ominnt F Synhronous Stte Grph K x=0 x=0 x= 0 z=0 x= z= Sketh the iruit. Stte 0 Stte 0 Stte Stte Stte= Stte only hnges on the lok ege Synhronous Stte Grph G x= x=0 = x= K = Stte Stte Stte Stte Show stte s well s Stte Stte 9 Summry So Fr: Summry So Fr Summry So Fr T flip flop En K R Re the question! ll of it! lwys hek for x + = Use this to simplify nywhere. lwys reue + x = + x Use nywhere exept for hzrs Too mny people sy x + = x 0 00 Put stte tles in K-mp orer To tell Moore from Mely in wor prolems. Moore Outputs Outputs will pper fter the next tive lok ege. 2. Mely Outputs Outputs will pper fter the input hnges Flip flops Smple D input just efore the lok.. Trnsfer this to the output just fter the lok. never hnges exept t lok eges T-flip flops Toggle fter every lok ege if - enle (provie it hs n enle) K D K D R D K Input using output Moore Mely 20

11 Summry So Fr: Summry So Fr Must Do ith Finite-Stte Mhines. Rerrnge the stte tle into Krnugh mp orer.. hnge sttes only t n tive lok ege. Often one when on timing igrms. NoNo. Rememer tht FSMs re multiple output mhines. th for shre gtes when you loop mps. Next-Stte ogi Output ogi D 2 D D 0 D 2 MU OGI: MU OGI MU OGI F= + e + e + + e Rell x + x = x x + x = x + F= 0 + e + e e F= + e + 0e + + e e + e +e + + e e e e e e e These MUs oth nee Use the sme input MU 22

12 MU OGI: MU OGI GOOD UK 23 MU OGI: MU OGI 24

13 MU OGI: MU OGI 25 MU OGI: MU OGI 26

14 MU OGI: MU OGI 27 MU OGI: MU OGI 28

15 MU OGI: MU OGI 29 MU OGI: MU OGI 30

16 MU OGI: MU OGI 3