Testing Digital Systems. CPE/EE 428, CPE 528 Testing Combinational Logic (3) Testing Digital Systems: Detection. Testing Digital Systems: Detection

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1 Tstin iit Systms CPE/EE 428, CPE 528 Tstin Comintion Loi (3) Comintion vs Squnti Systms W sh ovr omintion first Squnti iruits n tst usin omintion tst nrtion n sn hins Th stt FF sr onnt in shift ristr. Any vu n shift in (sttin n ritrry stt), th nt stt o, n thn shift out. Thus tsts n irty ppi to th omintion oi. FF s prtmnt of Etri n Computr Eninrin Univrsity of Am in Huntsvi Comintion oi Q Q o n/shift Q sn hin shiftin/out /4/23 VLSI sin II: VHL 2 Tstin iit Systms: ttion Tstin iit Systms: ttion N () A oo iruit N prous funtion () Assum 4 s-- (stuk-t, s) 2 3 ttin fut N f A tst vtor t is n ssinmnt of input vus. It tts fut f iff (t) f (t) f () A iruit with fut f prous iffrnt funtion f () Goo Ciruit Th st of tsts {T} tht tts f is foun y Futy Ciruit f () f () = /4/23 VLSI sin II: VHL 3 /4/23 VLSI sin II: VHL 4

2 Tstin iit Systms: ttion Tstin iit Systms: ttion tst for 4 s () f () = = (2 + 3) + 4 f = (2 + 3) > 4 = (+) =? = (+) + (+) = + + ( ) = = ((2+3)) 4 = () 4 = ( + ) 4 = = s-- / / / tst for 4 s -- Th omin oo/ iruit n rwn vus shown r for v/v f tht is, vus in th oo iruit / vus in th futy iruit v/ v f shows isrpny twn oo/futy iruit vus This sys tht ny input vtor with = n 4 = is tst vtor for 4 s--. 2 n 3 r on t-rs. /4/23 VLSI sin II: VHL 5 /4/23 VLSI sin II: VHL 6 Fut Ativtion n Proption Pth Snsitiztion s-- / / / tst for 4 s-- Two si onpts in fut ttion iustrt A tst must tivtth fut y rtin iffrnt v/v f vus t th fut sit thus 4 is ssin to. If it ry is stuk t zro, w know thr wi hn in iruit vus. A tst must propt th rror to primry output othr iruit vus must st to ow th oo/futy vu to sn t n output s-- / / / Snsitiz pth tst for 4 s-- Pth snsitiztion A in whos vu (with th tst t) hns in th prsn of fut f is si to snsitizto fut f y tst t ths ins r init y hvin iffrnt v/ v f vus A pth ompos of snsitiz ins is snsitiz pth /4/23 VLSI sin II: VHL 7 /4/23 VLSI sin II: VHL 8 2

3 Anothr mp Controin n Invrtin Vus Tst s s-- Asi Primitiv oi ts (AN, OR, NAN, NOR) n hrtriz y two prmtrs ontroin vu invrsion i Controin vu th vu whn on ny on input wi trmin th t s output rrss of th othr inputs (.. on ny AN t input) If on input hs th ontroin vu, th t s output wi i, whr n i om from th foowin t i AN OR NAN NOR /4/23 VLSI sin II: VHL 9 /4/23 VLSI sin II: VHL Controin n Invrtin Vus Controin n Invrtin Vus Aon th snsitiz pth ny input snsitiz to th fut wi hv vu, it othr inputs wi hv (ompmnt of ontroin vu) non-ontroin, or nin, vu th output wi hv vu i i AN OR NAN NOR / s-- / / i AN OR NAN NOR ou / / or or / / Whih r ontroin, whih r nin? /4/23 VLSI sin II: VHL /4/23 VLSI sin II: VHL 2 3

4 Tstin iit Ciruits: Runny Tstin iit Ciruits: Runny Fut f is tt if thr ists tst t tht tts it i.. (t) f (t) Howvr, f is untt if X Y F () = f () for Coo! Thr r som iruits whr vn if thr is fut in rtin ps, thy sti work! A iruit tht ontins n untt fut is runnt iruit. Th fut sit oviousy hs no fft on th iruit funtion Th iruit n simpifi you n rmov somthin! Emp: F = + + Is th fut Y s-- tt? Ativt n propt Y s-- /4/23 VLSI sin II: VHL 3 /4/23 VLSI sin II: VHL 4 Y s-- is untt F = + + = + Runny Th trm is runnt ovr in th Kmp it s not n ssnti impint of th funtion th othr two r Chn to iruit Gt Y n rmov from th iruit without fftin th oi funtion. Or you n kp it n hv som fut torn X Y trm is runnt /4/23 VLSI sin II: VHL 5 Runny Pro n Con Pro n Con Th fut is untt. This n oo! Th iruit sti works vn if thr r rtin futs in it. Ar othrs untt too? or hrr to tt Th runnt iruit rquirs tr hrwr tr r on th IC /4/23 VLSI sin II: VHL 6 4

5 Runny Pro n Con Th iruit is hzr fr on trnsition > Hzr th vu of th funtion tks on n intrmit vu iffrnt from th fin vu With non-runnt iruit, thr is hn of - - hzr With th runnt iruit, if th inputs hn from >, th output wi not o to zro. Ar thr othr suh trnsitions? Tstin iit Ciruits: Runny Rmovin runnt ovrs Untt fut Simpifition Ru AN (NAN) input s -- Rmov input AN (NAN) input s -- Rmov t, rp y () OR (NOR) input s- - Rmov input OR (NOR) input s- - Rmov t, rp y () z X Y Othr runnis Trip mour runny mtho for hivin fut torn. futs r orrt y ition oi mny futs wou untst thy utomtiy orrt n oi synthsis wou optimiz th runny wy! N tst mo to is orrtion /4/23 VLSI sin II: VHL 7 /4/23 VLSI sin II: VHL 8 Tstin: is it so simp? -Cuus Tst ninrs = Shrok Homs of th inustry Mthos for utomtiy nrtin tsts wr nssry Cotivy known s ATPG => Automti Tst Pttrn Gnrtion (tt) = / - rprsnts oi in th oo iruit n oi in th iruit (r ) = / - rprsnts oi in th oo iruit n oi in th iruit Fiv -vu oi:,,, r, X (on t r) /4/23 VLSI sin II: VHL 9 /4/23 VLSI sin II: VHL 2 5

6 -Cuus Truth ts for AN, OR, NAN, n NOR ts finitions Tst nrtion orithms work in trms of: Primry inputs (PI) ontro input to iruit. E.., pin on n IC, or n output of n FF in sn systm Primry outputs (PO) n osrv output of th iruit. E.., pin on n IC, or input to n FF in sn systm Justify, justifition th pross of stin PIs to for rtin in to hv spifi vu Propt, proption th pross of stin pproprit PIs tht ow isrpny to push to PO Tst nrtion orithms r out finin th pproprit PIs to ontro to tivt fut finin th pproprit PIs to ontro to propt th fut to on of th POs. /4/23 VLSI sin II: VHL 2 /4/23 VLSI sin II: VHL 22 Mor finitions Forwr impition f: Knowin on or mor t inputs, impy th output vu. Assum t inputs r th sm vu ithr or Thn th output is output = vu i W n rfin this if w know th ontroin vu i.. ony on of th inputs ns to hv to know output Bkwr impition f: Knowin th output n possiy som inputs, impy on or mor of th inputs Assum t inputs r th sm ithr or Thn th inputs r: inputs = output i W n rfin this if w know th ontroin vu If th input n to prou th output is, thn ony on input ns to hv it. /4/23 VLSI sin II: VHL 23 Justify Aorithm Justify (, v) Rursiv orithm to justify in to vu v = v if is primry input rturn you r on on this pth st n i to ontroin/invrsion vus of t rivin inv = v i if (inv == ) st on input j of t Justify (j, inv ) s for vry input j of t Justify (j, inv ) /4/23 VLSI sin II: VHL 24 6

7 An mp of justifition Tst Gnrtion: Propt Aorithm = v Prop (, rr) Propt vu rr from in if is primry input rturn you r on on this pth = rr st n i to ontroin/invrsion vus of t rivin if in is primry output rturn you r hom inv = v i if (inv == ) s st on input j of t Justify (j, inv ) for vry input j of t Justify (j, inv ) justify to B PO k = fnoutt of in,i = ontroin/invrsion vu of t k for vry input j of k othr thn Justify (j, ) Propt (k, rr i) Justify nin vus onto othr inputs k Propt furthr /4/23 VLSI sin II: VHL 25 /4/23 VLSI sin II: VHL 26 Tstin iit Ciruits Wht you know Fut mos wht n o wron n how w mo it physi n oi Bsi i of ttion tivt fut n propt to output Wht you on t know how to fiur out, systmtiy, whthr th who thin works how to ru th numr of futs to onsir whn nrtin tsts Toy Rviw quivn n fut opsin Bin tst nrtion orithms Bsi pproh sn so fr St in n fut in s--v Ativt th fut riv in to v stin th inputs n to st n intrn in to known vu is known s in justifition Ativtion rts isrpny Propt th fut isrpny Propt th isrpny on snsitiz pth to ny primry output / s-- ttion / Nottion: oo vu/ vu /4/23 VLSI sin II: VHL 27 /4/23 VLSI sin II: VHL 28 7

8 Fut ominn Equivn n ominn Summry Equivn vs. ominn ominn is spi s of fut quivn Fut quivn, if f () = () for thn th futs r funtiony quivnt. If this is tru for sust of, thn thr is ominn r tion ominn Lt T th st of tsts tht tt fut. A fut f omints th fut iff f n r funtiony quivnt unr T. Wht r th quivn sss? s-- s-- s-- s-- s-- s-- Equivn A, B, ominn omints A, B f (t) = (t) T is sust of T f for t in T,, /4/23 VLSI sin II: VHL 29 /4/23 VLSI sin II: VHL 3 Asi: Fut Lotion Ovr pross ttion ot us own to thr tsts W r ft with thr tsts for this t if w r intrst in fut ttion. If w r intrst in fut otion, w n mor To isot y s-- N to ppy oth n, on, tts th quivnt futs y s-- n z s--, on, tts th quivnt futs s-- n z s-- Tothr, thy n isot th thr futs (ssumin ony on fut tiv). fin fut mo st trt fut nrt tst for trt fut simut st of futs for iruit no mor futs: on s s y z s T isr tt futs T f /4/23 VLSI sin II: VHL 3 /4/23 VLSI sin II: VHL 32 8

9 Tst Gnrtion Towr n orithmi mns to nrt tst vtors Wht o w wnt in tst vtor? fut tivtion n proption if th isrpny wis (i.. from oo to ), thn so os th output how o w trmin if funtion hns with rspt to vri Us Automti Tst Gnrtion orithms (ATG) Primry inputs n outputs Tst nrtion orithms work in trms of: Primry inputs (PI) ontro input to iruit. E.. A pin on n IC, or n output of n FF in sn systm Primry outputs (PO) n osrv output of th iruit. E.. A pin on n IC, or input to n FF in sn systm Thy oprt in trms of: finin th pproprit PIs to ontro to tivt fut finin th pproprit PIs to ontro to propt isrpny to on of th POs. /4/23 VLSI sin II: VHL 33 /4/23 VLSI sin II: VHL 34 Propt, Justify A fw finitions justify, justifition th pross of stin PIs to for rtin in to hv spifi vu th vr justify on th input of t B th noun justifition is th pross of justifyin propt, proption th pross of stin pproprit PIs tht ow isrpny to push to PO propt th to ny output proption is th pross invovs justifition Impy you n Forwr impition f: Knowin on or mor t inputs, impy th output vu. Assum t inputs r th sm vu ithr or Thn th output is output = vu i W n rfin this if w know th ontroin vu i.. ony on of th inputs ns to hv to know output PIs B PO /4/23 VLSI sin II: VHL 35 /4/23 VLSI sin II: VHL 36 9

10 Look hin yoursf too Bkwr impition f: Knowin th output n possiy som inputs, impy on or mor of th inputs Assum t inputs r th sm ithr or Thn th inputs r: inputs = output i W n rfin this if w know th ontroin vu If th input n to prou th output is, thn ony on input ns to hv it. Justify Aorithm Justify (, v) Rursiv orithm to justify in to vu v = v if is primry input rturn you r on on this pth st n i to ontroin/invrsion vus of t rivin inv = v i if (inv == ) s st on input j of t Justify (j, inv ) for vry input j of t Justify (j, inv ) /4/23 VLSI sin II: VHL 37 /4/23 VLSI sin II: VHL 38 An mp of justifition Tst Gnrtion: Propt Aorithm = v if is primry input rturn you r on on this pth st n i to ontroin/invrsion vus of t rivin inv = v i if (inv == ) st on input j of t Justify (j, inv ) s for vry input j of t Justify (j, inv ) justify to Prop (, rr) Propt vu rr from in = rr if in is primry output rturn you r hom k = fnoutt of in,i = ontroin/invrsion vu of t k for vry input j of k othr thn Justify (j, ) Propt (k, rr i) k B PO Justify nin vus onto othr inputs Propt furthr /4/23 VLSI sin II: VHL 39 /4/23 VLSI sin II: VHL 4

11 Wi this wys work? Tst Gnrtion: Bsi Aorithm Wi justify n propt wys work? Ciruits without ronvrnt fnout st on n justify r h inpnnt of ny prvious justifition you r urnt tht proption n justify wi not intrfr Aorithm to tst in s--v in n st vus to (unknown) Justify in to vu v if (v == ) s Propt on in Propt on in Wi rquir mor justifition s-- /4/23 VLSI sin II: VHL 4 /4/23 VLSI sin II: VHL 42 Automti Tst-Pttrn Gnrtion (ATPG) Ronvrnt Fnout Tst U2.N for s-- ) Ativt (it) fut => U2.N = 2) Work kwr => A = 3) Work forwr (snsitiz th pth to PO) => U3.A2 =, U5.A2 = 4) Work kwr (justify outputs) => ABC = Fut U4.A s- -? Fut B s- -? Sin B rnhs n thn ronvrs t oi t U5. ATPG works. W rt two snsitiz pths tht prvnt fut from proptin to th PO. Th prom n sov y hnin A to, ut this rks rus of th ATPG! Th POEM orithm sovs th prom. /4/23 VLSI sin II: VHL 43 /4/23 VLSI sin II: VHL 44

12 Tst Gnrtion mp With ronvrnt fnout Fnout pths from t ronvr t som tr t Inputs n for proption my inonsistnt with ons n for justifition G2 G G3 G4 G5 s-- Prour: justify G to > === propt to G4 > rquirs G2 = ut = mks G2= Inonsistny rsh n urn Koom! /4/23 VLSI sin II: VHL 45 Tst nrtion mp, ont N to ktrk propt on othr pth G2 G G3 G4 G5 s-- Prour: justify G to > === propt to G4 > rquirs G2 = ut = mks G2= Inonsistny propt to G5 > ktrk justify G3 to this works with = /4/23 VLSI sin II: VHL 46 Bktrkin Mintinin th ision tr Bktrkin rquirs tht ision tr mintin Eh no sris sin s stt vus prviousy justifi on ins impitions, forwr n kwr Eh r sris nw ision justify in, tivt fut N to to o k to formr stt Stt A fi Stt A Stt Stt A2 fi Stt B win /4/23 VLSI sin II: VHL 47 Prop. to G4 Stt G2=, A = inonsistny fi Stt s justify G to Stt === A Prop. to G5 G3 = Stt = A2 win Prour: justify G to > === propt to G4 > rquirs G2 = ut = mks G2= Inonsistny propt to G5 > ktrk justify G3 to this works with = Bktrk, G2= no onr prt of sin stt. Rvrt to prvious stt. /4/23 VLSI sin II: VHL 48 2

13 Osrvtions on pproh Enumrtion us justify orithm ws rursiv Whn t hs ontroin vu on input, on pth st my n to ktrk n foow nothr vntuy, my n to foow Propt orithm ws rursiv Whn thr is fnout t proption point, on pth st towr output my n to ktrk n foow nothr vntuy, my n to foow Th ktrkin, in, is u to ronvrnt fnouts n prvious vus justifi on thm No soution? runnt wrt th fut As it turns out Th ntur stt mintnn in rursiv prorms n kp trk of th ision tr /4/23 VLSI sin II: VHL 49 Mor trminooy Whn proptin isrpny Oftn, u to fnout, thr r svr options Propt ns to pik on for th snsitiz pth - frontir Th -frontir is th st of ts with or on on or mor inputs n n on its output (no othr inputs r ontroin) This is th st from whih you st proption (snsitiztion) pth /4/23 VLSI sin II: VHL 5 -frontir -Frontir J-Frontir Bk to our mp G2 G G4 s-- In in justifition Th J-frontir is th st of ts whos output vus r known, ut th outputs r not impi (yt) y th inputs Som inputs my known, ut th urrnt output vu is not impi Simir to -frontir, ut ookin kwr G3 G5 Aftr th tivtion of th fut, n forwr impition, th - frontir is? If -frontir = Ø, thn no pth to primry output fiur, ktrk prvious justifitions hv m this pth impossi J-frontir /4/23 VLSI sin II: VHL 5 /4/23 VLSI sin II: VHL 52 3

14 J-Frontir Impition Rvisit Bk to th Emp G2 G G4 s-- Impition Pross Comput vus uniquy trmin y impition,,,, ookin forwr n kwr mor rssiv thn prvious impition mintin th n J frontir G3 G5 Th fut is tivt n forwr impition is on A t is st from th -frontir for proption In this s, G5 is th ony hoi Th J-frontir is thn? /4/23 VLSI sin II: VHL 53 /4/23 VLSI sin II: VHL 54 Bfor impition front Bkwr Impition nw impition front Aftr Bfor > > Forwr Impition > > Aftr < < < < < < J-frontir = { } J-frontir = {, } < < < > > > > > J-front={, } J-front={, } -front={, } -front={, } < > J-front={ } J-front={ } -front={ } > -front={ } /4/23 VLSI sin II: VHL 55 /4/23 VLSI sin II: VHL 56 4

15 Whr r w now? Pis of tst nrtion orithms sn justify, propt proms with ronvrnt fnout n to ktrk mks for mssir orithm n to kp trk of stt, n wht omintions hv n tri for. huristis to uss t st nt pth to foow To om orithm n vntuy Pom Impition Pross Rvisit Uniqu -riv If thr is ony on t on th frontir, thn impition propts throuh th t. It s th ony irtion ou propt for -frontir = {} < ftr -frontir = { } > /4/23 VLSI sin II: VHL 57 /4/23 VLSI sin II: VHL 58 A Pis in P Pis Controin n invrtin vus Fut tivtion Justifition Proption Forwr/kwr impition n J frontirs ision tr mintnn isussion of th orithm not tht this is vrsion of th orithm numr of situtions hv n ft opn,.. st n input, st t whih on? Initiiztion st in vus to X -Aorithm tivt th trt fut y ssinin oi vu to tht in. Propt to PO 2. Justify vus Impy_n_hk() os ony nssry impitions, no hois if -() == SUCCESS thn rturn SUCCESS s uno ssinmnts n its impitions /4/23 VLSI sin II: VHL 59 /4/23 VLSI sin II: VHL 6 5

16 Tst Gnrtion: Th Aorithm A iruit n fut to tst if (impy_n_hk() == FAIL) rturn FAIL if (rror not t primry output) { if (-frontir == Ø) rturn FAIL rpt { st n untri t (G) from -frontir = ontroin vu of G ssin to vry input of G with vu if (-A() == SUCCESS) rturn SUCCESS } unti ts from -frontir tri rturn FAIL} if (J-frontir == Ø) rturn SUCCESS st t G from th J-frontir = ontroin vu of G rpt { st n input (j) of G with vu, ssin to j if (-A() == SUCCESS) rturn SUCCESS ssin to j/* rvrs ision*/ } unti inputs of G r spifi rturn FAIL ort sin with known vus. Chk for inonsistnis. Push to primry output On t primry output, justify vus n to hv on th primry output s-- f f h i j k m n /4/23 VLSI sin II: VHL 6 /4/23 VLSI sin II: VHL 62 Trin throuh n mp Trin throuh n mp s-- f f h i j k m n s =, = = s-- f f h i j k m n s =, = = = isions Impitions Commnts = Ativt th fut h = = Uniqu -riv throuh = (th uniqu pth for ) = -frontir oms {i,k,m} isions Impitions Commnts = Propt throuh i i = = -frontir oms {k, m, n} /4/23 VLSI sin II: VHL 63 /4/23 VLSI sin II: VHL 64 6

17 s-- Trin throuh n mp h i j k = f f m j=k==m= isions Impitions Commnts Bn j=k= Propt throuh n =m= n= =, = k= But k = Contrition! -frontir rmins {k, m, n} n s =, = = /4/23 VLSI sin II: VHL 65 s-- Trin throuh n mp h i j k = f f m j=k==m= Bn isions Impitions Commnts = Propt throuh k k= = j= -frontir oms {m, n} s =, = = = /4/23 VLSI sin II: VHL 66 n s-- Trin throuh n mp f h i j isions Impitions Commnts =m= propt throuh n n = f = f = m = f k m = j=k==m= Bn But m =, ontrition! -frontir rmins {m, n} s =, = = =m= Bn = /4/23 VLSI sin II: VHL 67 n s-- Trin throuh n mp f h i j isions Impitions Commnts f = Propt throuh m m = f = = n = J-frontir is Nu f k m = j=k==m= Bn s =m= Bn = f =, n = prty! /4/23 VLSI sin II: VHL 68 n =, = = 7

18 Wht out th J-frontir? In this mp, inputs wr siy justifi throuh impition ssntiy,,, n f wr primry inputs if ths wr rivn y othr ts, th rir inputs miht not hv n impi... < J-frontir = { } J-frontir = {, } /4/23 VLSI sin II: VHL 69 Wht out th J-frontir? Th -orithm: piks t from th J-frontir n thn tris to st h input to ontroin vu If tht vu fis u to impy_n_hk, it is invrt n nw input is tri how os it hn th s whr non of th inputs shou ontroin? if (J-frontir == Ø) rturn SUCCESS st t G from th J-frontir = ontroin vu of G rpt { st n input (j) of G with vu, ssin to j if (-A () == SUCCESS) rturn SUCCESS ssin to j /* rvrs ision*/ } unti inputs of G r spifi rturn FAIL it hr if output of t G is justifi, possiy for sttin inputs /4/23 VLSI sin II: VHL 7 J-Frontir Anothr mp s Assum hn to th mp iruit Thn w wou ft with mnts in th J-frontir st J-frontir is {f} If th s r primry inputs, this is sy If thy r not primry inputs, mor ts in to show up in J-frontir you my not to st th input you st to th ontroin vu If thr is runny, th who pross miht fi. s-- f f h i j k m n -s h f j i isions impitions ommnts k ision Tr /4/23 VLSI sin II: VHL 7 /4/23 VLSI sin II: VHL 72 8

19 j -s f h i Anothr mp isions impitions ommnts =,=,=f= /4/23 VLSI sin II: VHL 73 k ision Tr tivt fut, uniqu riv h= i= prop throuh i. j,k= f; h=jf = j=, k= prop throuh j. f = nu. ktrk ( = ) j= =, k= prop throuh i, fut t output = justify h =, = = h= j= s = How os it work Conptuy Ativt fut n propt Summry: orithm Thn justify th rminin ts Whn proptin ssin to othr inputs of th ts on th snsitiz pth o forwr n kwr impition whn oin kwr, spify t inputs if thy r if on input shou, put t into J-frontir /4/23 VLSI sin II: VHL 74 s-- < Summry: orithm Summry: Aorithm Oh, y th wy justify th rst of ths inputs Tht is, th -frontir is pursu with ony prti rr to whthr th vus st r sf onsistnt In th pross, th J- frontir rw r 5 ts shown hihiht pus th ts tht riv thm n thr s ots of ronvrnt fnout to us justifition proms. s-- iruit mss up to mk point pth-first push towr primry output o justifition n onsistny ftrwr s n kwr impition n us proms us ktrkin s nssry Ehustiv, ponnti Th numr of oprtions prform is n ponnti funtion of th numr of ts This is worst s, typiy ony sn whn fut turns out to untt But you on t know it s untt unti you hustivy try vrythin Huristis for stin on of hp ru srh tim of sussfu srhs Tst nrtors r oftn imit in thir srh pth, thus som tt futs on t hv tsts. /4/23 VLSI sin II: VHL 75 /4/23 VLSI sin II: VHL 76 9