CS2204 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2014

Transcription

1 CS22 DIGITAL LOGIC & STATE MACHINE DESIGN SPRING 2 DUE : Ferury 27, 2 HOMEWOR II READ : Relte portions of Chpters III, IV n VI. ASSIGNMENT : There re eight questions two of whih re from the textook. Solve ll homework n exm prolems s shown in lss n pst exm solutions. ) Consier the following omintionl iruit with four inputs n three outputs : ms ms z2(,,, ) z(,,, ) z(,,, ) is 2-it 2 s Complement Binry numer is 3-it 2 s Complement Binry numer Opertion Tle Opertion = 2 = = + = - (i) Otin the truth tle of the omintionl iruit se on the opertion tle. In single sentene n you esrie wht this iruit oes, i.e. its purpose? In orer for to hve three its so tht it hs the sme its s, ssume tht hs n invisile thir (leftmost) it whose vlue is otine vi sign extension on. Then perform the neessry opertion on. Nme this invisile leftmost it s e n show it on your truth tle. (ii) Then, otin the minterm lists of the outputs from the truth tle. 2) Consier the omintionl iruit elow with 8 inputs n 3 sets of outputs. M Comintionl Ciruit n M re BCD igits R y z M -it ADDer (9) S out B A A>B A=B A<B -it Unsigne Binry Comprtor y R z Anlyze the iruit to otin its purpose. The purpose must inlue the mening of eh output (R, y n z). NYU Shool of Engineering Pge of 2 Hnout No : 6 Ferury 3, 2

2 Note tht there re 8 inputs therefore truth tle is imprtil. You re suggeste tht you otin n opertion tle tht lssifies input omintions into few possiilities. 3) Consier Question 2 ove. Implement the two loks (the ADDer n omprtor) in the figure, y using minimum numer of TTL LS hips. Drw the full shemti y hn, showing ll the onnetions. By using green pen, outline the two loks in your shemti. ) Develop mjority iruit with four single-ril inputs, A, B, C, D, n one output. It works suh tht if three or more inputs re, the output is. Otherwise, (ll inputs re or one input is or two inputs re ), the output is. A B C D Mjority Comintionl Ciruit f(a, B, C, D) Í First, otin the truth tle of the funtion. Í Seon, implement the funtion y using single 7LS5 hip. No other gte or hip n e use. 5) Consier the following iruit with four single-ril inputs : ms Digitl iruit f(,,, ) f(,,, ) = m(2, 6,, ) Implement the iruit y using single 7LS38 hip n one generi gte 6) Solve Prolem 3.3. The question is sking this : Your frien tells you to hol CMOS hip. Woul you hol the hip? Why? NYU Shool of Engineering Pge 2 of 2 CS22 Hnout No : 6 Ferury 3, 2

3 7) Solve Prolem 6.7 () n (). For prt (), you will hek your notes, serh igitl logi ooks n TTL t mnuls to see whih hip hs the given internl iruit. For Prt (), you will otin n opertion tle to nswer the textook question : Wht oes the iruit o? 8) Consier the Ppm term projet. The grph of the plying strtegy of n imginry mhine plyer is s follows : Ply on the (rightmost) lrgest jeny position (iretly if equl) Consier the following tle tht shows the rnom igit, position isplys efore n fter the mhine plyer plys, whether the rnom igit is plye iretly or e, the numer of jenies, the points erne y the mhine plyer n whether the mhine plyer plys gin : RD Displys Before Ply PD3 PD2 PD PD Displys After Ply PD3 PD2 PD PD D/A The Ajeny Points Erne (Deiml) Mhine plyer plys gin? 6 7 C 6 E F C E 5 A 9 Assume tht the oe is F6. The mening of D/A is Diret/A whih is whether the mhine plyer plys the rnom igit iretly on position or y ing to position. A irle is rwn on position if it is plye on. Note tht the ses re inepenent of eh other. Tht is, they o not neessrily follow eh other with respet to time. Work on the rows. RELEVANT QUESTIONS AND ANSWERS Q) Consier the following iruit tht ompres its 8-it 2 s Complement input with n 99 n hs two tivelow outputs. The lk ox view n opertion tle of this sulok re shown elow : NYU Shool of Engineering Pge 3 of 2 CS22 Hnout No : 6 Ferury 3, 2

4 8 Compre with & 99 L G99 Inputs Opertion < L = n G99 = < < L = n G99 = > 99 L = n G99 = Output L is when input is less thn zero. Output G99 is when input is greter thn 99. Sine there re eight inputs, we prtition the lk ox into two loks se on the ove opertion tle ove : 8 Compre 8 Compre L G99 with with 99 Implement the Compre with 99 lok. Follow the proeure given in lss : You will implement eh susulok of the lok y using few TTL LS hips for the se eveloping new PCB. A) Below we show the 2 s Complement representtion of eiml numer 99 n the simplifie truth tle : 99/2 = 9 & ls 9/2 = 2 & 2/2 = 2 & 2/2 = 6 & 6/2 = 3 & 3/2 = & / = & ms () 2 Unsigne () 2 2 s Complement positive numers negtive numers G x x x x x x x neg The TTL hip 7LS682 is n 8-it unsigne omprtor hip with tive-low P=Q n P>Q outputs. While it n ompre 8 its, it nnot ompre 2 s Complement numers. For exmple, when is negtive, the omprtor interprets it numer etween 28 n 255 in eiml. However, heking if the numer is negtive n ypssing the omprtor hip is simple y using n OR gte. The gte output woul e the G99 output. The gte woul output if 7 is ( is negtive), otherwise, its output woul epen on the omprtor output : P7 P6 P5 P P3 P2 P P Q7 Q6 Q5 Q Q3 Q2 Q Q 7LS682 P=Q P>Q G99 NYU Shool of Engineering Pge of 2 CS22 Hnout No : 6 Ferury 3, 2

5 Q2) Consier the following 5-input, -output iruit : j Comintionl Ciruit R is -it 2 s Complement Binry numer Its lok prtitioning is shown elow : Inrement Ciruit Tking 2 s Complement Ciruit Selet Ciruit (-it 2-to- Selet Ciruit) R j selet Anlyze the iruit to otin its purpose. In orer to o tht first, otin the opertion tle se on the given loks ove. For eh lok, there is mjor opertion on the opertion tle. Bse on the mjor opertions erive the textul input-output reltionship n then the purpose of the iruit. A2) The opertion tle n the loks re s follows : Input Opertion j = R = ( + ) j = R = 2 From the opertion tle we see tht the mjor opertions re () inrementing 2 (tht is, + ), (2) tking the 2 s omplement of () n (3) seleting the output of one of these two opertions. Hene, we hve one lok for eh mjor opertion This iruit is n Arithmeti Unit tht inrements or negtes -it numer input. Q3) Consier the following 5-input, -output iruit n its opertion tle : Comintionl R j Ciruit n R re -it 2 s Complement Binry numers Sitution Opertion j = R = + j = R = 2 If is the mx vlue (7), then R = + is the min vlue (-8) The following lok prtitioning is suggeste se on the opertion tle : NYU Shool of Engineering Pge 5 of 2 CS22 Hnout No : 6 Ferury 3, 2

6 j Invert Ciruit Selet Ciruit (-it 2-to- Selet Ciruit) selet -it ADDer Ciruit R i) Prove tht this prtitioning with three loks is orret. Tht is, prove tht the three loks implement the opertion tle. ii) Then, implement the three loks y using minimum numer of high-ensity TTL LS hips. n generi gtes Drw the full iruit y showing ll the onnetions. By using otte lines, outline the three loks in your iruit. iii) Mention the high-ensity TTL hip usge. A3) i) We know tht tking the 2 s omplement of numer is the sme s omplementing it n ing. Thus the opertion tle eomes s follows : Sitution Opertion j = R = + 2 j = R = = + ) When j is, the MUX selets whih is e y the -it ADDer to generte + ) When j is, the MUX selets, generte y the invert iruit n is e y the -it ADDer to generte the other output vlue + Thus, the prtitioning is orret, it implements the opertion tle. Note tht there is nother prtitioning given in Pst Exm Question 2 ove. ii) The implementtion of the omintionl iruit y using TTL hips is shown elow. We use TTL MUX hip 7LS57 n TTL ADDer hip 7LS83. The 7LS83 hip is -it hip with the sme funtionlity s the 7LS283 hip. In ition, we use four generi gtes I I I I I I I I -it 2-to- MUX Y Y Y Y S E in A3 A2 A A B3 B2 B B -it ADDer S3 S2 S S out R3 R2 R R j NYU Shool of Engineering Pge 6 of 2 CS22 Hnout No : 6 Ferury 3, 2

7 iii) The hip usge is s follows : 7LS57 -it 2-to- MUX 7LS83 -it ADDer generi gtes 2 TTL hips use. generi gtes use Q) A omintionl iruit ompres two 3-it 2 s omplement numers, n M. Numer is represente y its, n. Numer M is represente y its, e n f. The two tive-high outputs, z n z re for = n <, respetively. The lk ox view of the omprtor is s follows : M e f ms ms 3-it 2 s omplement omprtor z ( = M ) z ( < M ) Design this 2 s omplement omprtor y using only inverters, n the following two hips : 3-it ADDer n - to- MUX : ms ms IA2 IA IA IB2 IB IB in 3-it ADDer r r r2 out ms ms S S I I I2 I3 -to- MUX Y Assume tht no overflow will our uring the itions. Explin how you use the hips. Do not use ny other/itionl hips/gtes/flip-flops. A) To ompre the two numers, n M, we hve to sutrt M from : - M - M = + (-M) = + M + To sutrt M, we omplement M its,, e n f. Also, we input to the in input of the ADDer. If < M, the sign it of the sutrtion result is, sine the result is negtive. Thus, the r2 output of the ADDer is the z output of the omprtor. If is equl to M, the sutrtion result is. It is etete zero y onneting the r2, r n r outputs of the ADDer to the -to- MUX. The output of the MUX is the z output of the omprtor. As seen elow, the r n r outputs selet the r2 output when they re zero. If r2 is lso, the output of the MUX shoul e. Tht is why n inverter is neee to invert r2. The other t inputs of the MUX re onnete, for ses where is not equl to M : NYU Shool of Engineering Pge 7 of 2 CS22 Hnout No : 6 Ferury 3, 2

8 e f ms ms IA2 IA IA IB2 IB IB in 3-it ADDer r r r2 out ms ms S S I I I2 I3 -to- MUX Y ( = M) z ( < M) z Q5) Consier the omintionl iruit with four inputs n three outputs elow. : & R re 2 s Complement Binry numers ms ms vli(,,, ) y(,,, ) R z(,,, ) Opertion R = + ; vli = if overflow R = - ; vli = if overflow y = ; z = ; vli = y = ; z = ; vli = (i) Otin the truth tle of the iruit se on the opertion tle. (ii) Then, otin the minterm lists of the outputs from the truth tle. A5) The truth tle n the minterm lists : vli y z The Minterm lists : vli(,,, ) = m(, 2, 3,, 5, 7, 8, 9,,, 2, 3,, 5) y(,,, ) = m(, 2,, 7, 9,, 3, 5) z(,,, ) = m(, 2,, 6,, ) NYU Shool of Engineering Pge 8 of 2 CS22 Hnout No : 6 Ferury 3, 2

9 Q6) Consier the omintionl iruit with four inputs n four outputs elow. G ms ms z3(,,, ) z2(,,, ) z(,,, ) z(,,, ) G is 3-it 2 s Complement Binry numer is -it 2 s Complement Binry numer If = then = G - else = G + (i) Otin the truth tle of the omintionl iruit se on the textul input/output reltionship. In orer for G to hve four its so tht it hs the sme its s, ssume tht G hs n invisile fourth (leftmost) it whose vlue is otine vi sign extension on G. Then perform the neessry opertion on G. Nme this invisile leftmost it s e n show it on your truth tle. (ii) Then, otin the minterm lists of the outputs from the truth tle. A6) The truth tle n minterm lists re s follows : G G e z3 z2 z z The Minterm lists : z3(,,,) = m(,, 5, 6, 7, 2, 3, ) z2(,,,) = m(, 5, 6, 7,, 2, 3, ) z(,,,) = m(, 3,, 7, 9,, 3, ) z(,,,) = m(, 2,, 6, 8,, 2, ) Q7) Consier the following omintionl iruit with four inputs n four outputs : & R re 2 s Complement Binry numers ms ms w(,,, ) x(,,, ) y(,,, ) z(,,, ) R Opertion R = - (negte ) R = 2 * (two times ) R = * (four times ) R = * ( times ) NYU Shool of Engineering Pge 9 of 2 CS22 Hnout No : 6 Ferury 3, 2

10 (i) Otin the truth tle of the iruit se on the opertion tle. Use sign extensions to otin its of R from 2 its of s one in the homework. (ii) Then, otin the minterm lists of the outputs from the truth tle. A7) The truth tle n the minterm lists : e f w x y z The Minterm lists : w(,,, ) = m(, 6, 7,, ) x(,,, ) = m(, 6, 7, 9,, ) y(,,, ) = m(, 2, 5, 7) z(,,, ) = m(, 3, 3, 5) Sine input hs two its n output R hs its, we sign exten input y two its. These new leftmost two its of re e n f n their vlues re shown on the truth tle ove. Q8) Consier the -input, -output iruit n its gte network shown elow. ms Comintionl Ciruit ms y3 y2 y y R n R re -it Unsigne Binry numers y3 q y2 p y y Anlyze the gte network to otin the opertion tle n then etermine its purpose. In orer to o tht ontinue with the truth tle elow from whih the purpose n e otine : NYU Shool of Engineering Pge of 2 CS22 Hnout No : 6 Ferury 3, 2

11 p q y3 y2 y y R A8) We ontinue with the truth tle elow : p q y3 y2 y y R Opertion Tle : Sitution Opertion is even R = is o R = + The purpose is tht when is even, the output is equl to. Otherwise, the output is equl to +. In the se of = 5, the output is whih is norml sine 5 + = 6 tht requires 5 its n its rightmost four its re zero. NYU Shool of Engineering Pge of 2 CS22 Hnout No : 6 Ferury 3, 2

12 Q9) Consier the following swithing funtion whose minterm list is given elow : y(,,, ) = m(, 3,, 5, 7,, 2, 3,, 5) Implement the funtion y using single hip : just one 7LS5 MUX hip s one in lss. Assume tht there re single-ril inputs. A9) The funtion is implemente y using single 7LS5 hip : z : z(,,, ) = m(, 3,, 5, 7,, 2, 3,, 5) I I I2 I3 I I5 I6 I7 7LS5 E S2 S S z(,,, ) Q) Consier Mro 3, M3, of Blok 6 of the term projet. It hs 6 inputs n three outputs. In lss it is prtitione into two piees. One piee heks whih of the four isplys re zero. The other piee etermines the rightmost zero isply n outputs the two ERODISP lines. Implement the piee tht genertes the ERODISP lines y using lss notes n y using minimum numer of smllest TTL MUX hips s shown in lss. Assume tht there re only single-ril inputs. Agin, you will use only TTL MUX hips. No other hip or gte n e use. A) We nee to use 6-to- MUX for eh funtion to gurntee not to use n inverter. We n use n 8-to- MUX if we o not nee n inverter. But, we see tht oth funtions re zero when is. Thus, we n use the input s n enle input to isle the outputs when it is. We n then use -to- MUX if we refully etermine the selet inputs. Sine there is TTL -to- MUX with two MUXes, we then nee just one TTL MUX hip : 7LS53 : NYU Shool of Engineering Pge 2 of 2 CS22 Hnout No : 6 Ferury 3, 2

13 y(,,, ) = m(, 8, 2) + () z(,,, ) = m(2, 6, 8,, ) + () x x S S E I o I I 2 I 3 E I o I I 2 I 3 7LS53 Chip Usge : 7LS53 2-it -to- MUX Totl : hip use y z Q) Anlyze the igitl iruit with four single-ril inputs n two outputs elow. Otin the truth tle of the two funtions, f(,,, ) n g(,,, ). Then, etermine the purpose of the iruit. ms The lk ox view : Digitl iruit f(,,, ) g(,,, ) The internl iruit : I I 7LS5 I2 I3 I I5 I6 I7 E S2 S S f(,,, ) g(,,, ) A) A igitl iruit is given n its truth tle n the purpose re ske. Sine the 7LS5 is n 8-to- MUX, we n get the -mp of the funtion from whih truth tle n e otine. In ition n re the omplement of eh other, therefore, otining the rnugh mp of output is enough to otin the omplete truth tle. NYU Shool of Engineering Pge 3 of 2 CS22 Hnout No : 6 Ferury 3, 2

14 I I 7LS5 I2 I3 I I5 I6 I7 E S2 S S f(,,, ) g(,,, ) : = f(,,,) = m(,,5,8,9,,2,3,,5) = g(,,,) = m(,2,3,6,7,) The truth tle of the funtions : f(,,,) g(,,,) f(,,,) g(,,,) The minterm list for f(,,, ) is ientil to the minterm list of iruit stuie in lss : the 2-it unsigne omprtor. By stuying the tle, one onfirms it is orret. The iruit then ompres two 2-it unsigne numers where : - f(,,, ) outputs - when G = (, ) is greter thn or equl to H = (,) - g(,,, ) outputs - when G = (, ) is less thn H = (, ) Q2) Consier the following minterm list : f(,,, ) = m(, 3, 8, 9,, ) + (, 5, 6, 3) Implement the funtion y using single 7LS38 DCD hip n one TTL SSI hip s one in lss. Inite the TTL hip usge. Assume tht there re only single-ril inputs. A2) Sine we hve four inputs, we nee -to-6 eoer. But, we re ske to use 7LS38 hip whih is 3- to-8 eoer hip! In orer to figure out how we n use the 3-to-8 eoer for this pplition, we nee to exmine its rnuh mp. We see tht the funtion is when input is n so 3-to-8 Deoer woul work. We see tht the funtion must output when (,, ) is () or omintion 2. The iruit is then s follows : NYU Shool of Engineering Pge of 2 CS22 Hnout No : 6 Ferury 3, 2

15 f(,,, ) = m(, 3, 8, 9,, ) + (, 5, 6, 3) The funtion n e esrie in terms of, n when is s follows : X X X X X f(,, ) = m(, 3,, 5, 6, 7) + () Then, the iruit with 7LS38 eoer hip is s follows : The hip usge : 7LS38 3-to-8 Deoer hip use. 7LS38 A2 A A E E2 E3 Y Y Y2 Y3 Y Y5 Y6 Y7 f(,,, ) Q3) Consier the following minterm list : f(,,, ) = m(,, 5, 6, 9, ) + (7,, 3) Implement the funtion y using single hip : just one 7LS5 MUX hip s one in lss. Assume tht there re only single-ril inputs. No other hip/gte n e use. A3) f(,,, ) = m(,, 5, 6, 9, ) + (7,, 3) X X X I I I2 I3 I I5 I6 I7 7LS5 E S2 S S f(,,, ) Chip Usge : 7LS5 8-to- MUX Totl : hip use NYU Shool of Engineering Pge 5 of 2 CS22 Hnout No : 6 Ferury 3, 2

16 Q) Implement the following iruit with three single-ril inputs y using 7LS38 hip n gtes : ms Digitl iruit f(,, ) f(,,) = m(2, 3, 5, 7) A) The 7LS38 eoer hip hs tive-low outputs n so we nee NAND gte : 7LS38 A2 A A E E2 E3 Y Y Y2 Y3 Y Y5 Y6 Y7 f(,, ) Q5) Implement the following iruit with four single-ril inputs y using 7LS38 hip n one generi gte : ms Digitl iruit f(,,, ) f(,,, ) = m(,, 3, 5) A5) Sine we hve four inputs, we nee -to-6 eoer. However, we re ske to use 7LS38 hip whih is 3-to-8 eoer hip! In orer to figure out how we n use the 3-to-8 eoer for this pplition, we nee to exmine its rnugh mp : f(,,, ) = m(,, 3, 5) We relize tht the funtion is zero when is. Tht is, for input omintions,, 2, 3,, 5, 6 n 7, the output is zero. When is, the output epens on the other inputs, n. Tht is, when is, the funtion n e esrie in terms of, n s follows : f(,, ) = m(2, 3, 5, 7) NYU Shool of Engineering Pge 6 of 2 CS22 Hnout No : 6 Ferury 3, 2

17 We n then use input to enle the eoer when is. The remining three inputs ontrol the eoer t inputs. Then, the iruit with 7LS38 eoer hip n one NAND gte is s follows : 7LS38 A2 A A E E2 E3 Y Y Y2 Y3 Y Y5 Y6 Y7 f(,,, ) Q6) Consier the omintionl iruit whose lk-ox view n input/output reltionship re shown elow. ms y y is, if is ivisile y three (3) y y is, if is ivisile y five (5) is Unsigne Binry Implement the iruit y using one minimum size TTL Deoer hip n minimum numer of TTL SSI hips. Your nswer will inlue (i) the truth tle, (ii) the minterm lists, (iii) the iruit, n (iv) the TTL hip usge. A6) The truth tle is s follows : y y The minterm lists re s follows : y (,, ) y (,, ) = = m(, 3, 6) m(, 5) The iruit with the TTL hip usge is s follows : NYU Shool of Engineering Pge 7 of 2 CS22 Hnout No : 6 Ferury 3, 2

18 7LS38 A2 A A E E2 E3 Y Y Y2 Y3 Y Y5 Y6 Y7 y (,,, ) y (,,, ) We eie to use 3-input NAND gte s 2-input NAND gte The hip usge : 7LS38 3-to-8 Deoer 7LS w/3 3-input NANDs, gte unuse 2 hips use. gte unuse Q7) Consier the Ppm term projet. The flowhrt of the plying strtegy of mhine plyer is s follows : Ply on the rightmost lrgest jeny position (iretly if equl) N Lrgest jeny is? Y Lrgest regulr rewr is < 5? Ply on the rightmost lrgest regulr rewr points position (iretly if equl) N Y Skip Consier the following tle tht shows the rnom igit, position isplys efore n fter the mhine plyer plys, whether the rnom igit is plye iretly or e, the numer of jenies, the points erne y the mhine plyer n whether the mhine plyer plys gin : RD Displys Before Ply PD3 PD2 PD PD Displys After Ply PD3 PD2 PD PD D/A The Ajeny Points Erne (Deiml) Mhine plyer plys gin 8 C C C C C A 2 8 Yes 9 E F F F F 6 A A E A A E Assume tht the oe is. The first row shows how the rnom igit is plye y the mhine plyer. A irle is rwn on position if it is plye on. The mening of D/A is Diret/A whih is whether the plyer plys the rnom igit iretly on position or y ing to position. Note tht the ses re inepenent of eh other. Tht is, they o not neessrily follow eh other with respet to time. Continue with the remining rows. NYU Shool of Engineering Pge 8 of 2 CS22 Hnout No : 6 Ferury 3, 2

19 A7) RD Displys Before Ply PD3 PD2 PD PD Displys After Ply PD3 PD2 PD PD D/A The Ajeny Points Erne (Deiml) Mhine plyer plys gin 8 C C C C C A 2 8 Yes 9 E E D 2 36 Yes 3 F F F F F F F F Skip Skip Skip Skip 6 A A 6 A D 2 Yes E A A E A D 76 Yes E D 3 56 Yes Note tht the mhine plyer oes not hek for oe igits n so misses lrge rewr point on row. The rnom igit on this row enle it to ply oe igit. The mhine plyer erns lrge mount of rewr points on row 5 y plying oe igit ientlly. Q8) Consier the Ppm term projet. The flowhrt of the plying strtegy of n imginry mhine plyer is elow: Y RD =? N Ply on the rightmost lrgest regulr rewr position (iretly if equl) Y Any jeny? N Ply on the rightmost lrgest jeny position (iretly if equl) Ply on the rightmost lrgest isply position iretly Consier the tle elow tht shows the rnom igit, position isplys efore n fter the mhine plyer plys, whether the rnom igit is plye iretly or e, the numer of jenies, the points erne y the mhine plyer n whether the mhine plyer plys gin. RD Displys Before Ply PD3 PD2 PD PD Displys After Ply PD3 PD2 PD PD D/A The Ajeny Points Erne (Deiml) Mhine plyer plys gin A C 3 A C D 8 Yes F F E 9 E F 5 C 7 F E 6 2 NYU Shool of Engineering Pge 9 of 2 CS22 Hnout No : 6 Ferury 3, 2

20 Assume tht the oe is E2. The first row shows how the rnom igit is plye y the mhine plyer. A irle is rwn on position if it is plye on. The mening of D/A is Diret/A whih is whether the plyer plys the rnom igit iretly on position or y ing to position. Note tht the ses re inepenent of eh other. Tht is, they o not neessrily follow eh other with respet to time. Continue with the remining rows. A8) RD Displys Before Ply PD3 PD2 PD PD Displys After Ply PD3 PD2 PD PD D/A The Ajeny Points Erne (Deiml) Mhine plyer plys gin A C 3 A C D 8 Yes F D 2 Yes F E F E A 5 No 9 E F 5 C E F 5 5 D Yes 7 F F D Yes 8 2 E E E 2 A 25 Yes The mhine plyer strtegy oes not hek for oe igits n so misses to ern oe rewr points when the rnom igit is 9 n ove. On the other hn, y hne it erns oe rewr points when the rnom igit is 2 n 8 ove NYU Shool of Engineering Pge 2 of 2 CS22 Hnout No : 6 Ferury 3, 2