VLSI Testing Assignment 2

Transcription

1 1. 5-vlu D-clculus trut tbl or t XOR unction: XOR 0 1 X D ~D X D ~D X ~D D X X X X X X D D ~D X 0 1 ~D ~D D X 1 0 Tbl 1: 5-vlu D-clculus Trut Tbl or t XOR Function Sinc 2-input XOR t wors s comprtor or prity ccr, outputtin 0 wn t inputs r t sm n 1 wn ty r irnt, it is ncssry to now bot vlus t t inputs in orr to vlut t output. I on vlu is not nown, ow cn t t compr it to t otr vlu? Simply, it cnnot. Tus, or ll css wr n input is unnown t output is unnown. s suc t X inputs l to X outputs. Wn on input s t vlu 0, t output will b t sm s t vlu o t otr input. 0 n 1 ivs 1, 0 n ~D ivs ~D, n so on. Wn on input s t vlu 1, t output will b t complmnt o t vlu o t otr input. 1 n 0 ivs 1, 1 n ~D ivs D, 1 n 1 ivs 0, n so on. T rminin css r tos wn bot inputs r itr D or ~D. s t XOR t wors s comprtor, i bot vlus r t sm, t output will b 0. Tis is tru wn bot inputs r itr D, or bot inputs r ~D. Wn bot inputs r irnt t output will b 1, suc is t cs wn on input is D n t otr is ~D. 2. Primitiv ub or XOR XOR Tbl 2: Primry ub Tbl or 2 Input XOR Gt s cn b sn in t bov tbl Tbl 2 tr is no minimiztion possibl in inin t Primry ubs o n XOR t. ll ntris r rquir, s n unnown t t input rsults in n unnown output, s sown bov Tbl 1. P 1 o 7

2 Primitiv ub or 2:1 MUX Sl Output Tbl 3: Trut Tbl or 2:1 MUX Sl Output 0 X 0 0 X X X 0 1 Tbl 4: Primry ub Tbl or 2:1 MUX s cn b sn in t bov tbl, t slction lin must b ctiv to t n output. T input tt psss trou t multiplxor ccorin to t slct lin must b spcii. T otr inconsquntil input cn b ny vlu, rprsnt by n X in t tbl bov. 3. s w r tstin or stuc-t-1 ult t t no, w cn st t vlu o tis no to: = D P 2 o 7

3 W n to riv tis D vlu to Primry Output PO. It is ssum tt sinc nos,, n r lbl irntly tt ty cn b isjoint. s in t cs r, wr is s--1 n n unction normlly. s suc, it is impossibl to riv t D vlu to t output. Tror, w will riv t D vlu to. Tus, = D W cnnot stblis wt t output t is s it pns on t vlu o. Eitr 1 or 0 or is vli s tis will rsult in n output o D or ~D or, rspctivly. W r, now, t t stp wr w must o t justiiction by bc proptin our st vlus. W now tt in orr to tst i is s--1: = = 0 In orr to civ t prvious conition, w n = = 0 In orr or = 0, w n = = 1 In orr or = 0, sinc = 1, w n = 1 In orr or to not b qul to 0, w n = 1 In orr or = 1, w n or n to b irnt. s w v prviously stblis tt = = 1, w cn s tt t ult is runnt, n cnnot b tst or. nswr: Tr r no vctors to tst tis ult s it is runnt. 4. PODEM Mto or prormin src or no s--1. ccorin to my uristics blow t orr is s ollows: 1 0 F1 D 1 0 F2 F3 FX is trminl stt rsultin in no tst vctor. P 3 o 7

4 F1 is u to t ct tt bin 1 orcs to vlu o 1, wic os not tst or t s--1 conition soul b 0. F2 is u to t ct tt D bin 1 orcs to vlu o 1, wic os not tst or t s--1 conition soul b 0. F3 is u to t ct tt bot n D bin 0 os not llow or t vlu t to b pss to nitr nor. Tus, t s--1 ult cnnot b tst or s t D-vlu t tis no cnnot b pus orwr to PO rrlss o t PI vctors. s--1 is runnt ult. b T uristics us or prt wr s ollows: ssin t primry inputs PI tt irctly inlunc t vlu t t no unr tst. Do tis in orr to st to t rit conition: 1 or s- -0 ults, n 0 or s--1 ults. Ts PIs r n D. s t prvious stp prov tt t ult ws runnt, t nxt stps r moot. I will, owvr, inict t uristics tt woul v bn us t prvious stp not il. Onc, t no unr tst s bn snsitiz, stblis snsitiz pt to t primry output PO, wic woul v rquir us ssinin vlus to itr or, or n. Finlly, t inputs tt sm to ct t pt to t output most inirctly woul v bn ssin, E n F. ll tis woul v l to tst vctor, t ult not bn runnt. 5. Drivin lobl implictions or t SORTES loritm, will not b on or trivil css wic only spn on t. =1 =1 m=1 p=0 =1 =1 m=1 q=1 Tror, =1 p=0. n, =1 q=1. n, =1 m=1. D=1 =1 m=1 p=0 D=1 =1 m=1 q=1 Tror, D=1 p=0. n, D=1 q=1. n, D=1 m=1. =0 m=0 =0 u=0 =1 w=1 Wit mous ponns, w cn lso in t ollowin implictions, p=1 =0 q=0 =0 P 4 o 7

5 m=0 =0 p=1 D=0 q=0 D=0 m=0 D=0 m=1 =1 u=1 =1 w=0 =0 It ws notic tt no r is st to 0 no mttr t input vctor. I is 1, tn p is 0, wic orcs r to 0. Eqully, i is 0, tn r is ncssrily 0. Tus, ny nlysis o implictions t no r is irrlvnt s w now t vlu o tis no rrlss , n r consir s sprt nos in orr to b bl to istinuis btwn t intrnl nos o n, n t Primry Output PO,. 1 ND : 2 NND : 3 OR : 4 XOR : 5 ND : 6 XOR : Extrs: P 5 o 7

6 P 6 o 7 In orr to tst t no s--0, w n to s on Primry Output to b inlunc by tis. s t primry outputs r n, n no is isolt rom no unlss pssin trou no wic is inrntly lin to, it is only ncssry to us output s t obsrvtion point. Tus, ll o no n t circuit lin to it not pssin trou no cn b omitt. I v writtn out t ull ST cluss blow, n tn t ruc st o cluss wic r t only ons rquir or inin vctor to supply n obsrvbl inlunc t on primry output. Lrrb inicts tt rmovin cluss is not problm provi w r urnt tt rmovin t vribl will not cus stisibl ormul to ppr to b n unstisibl on. [Lrrb p 8] ST luss: Goo ircuit 60 Litrls: Fulty ircuit 34 Litrls: ctiv lus 45 Litrls: Fult sit n Gol 5 Litrls: Notic ow it is ncssry to inclu t brncs, n. I w i not, it woul not v bn s stritorwr to crctriz t ctiv lus, s t 3 litrl clus is ncssry to stblis tt is Primry Output, n tt ls to notr PO. Tus, itr cn b ctiv in orr to obsrv t prsnc o ult.

7 Ruc ST luss: Goo ircuit 52 Litrls: Fulty ircuit 26 Litrls: ctiv lus 30 Litrls: Fult sit n Gol 5 Litrls: Finin vctor: To stisy t ult sit cluss, w rquir: = 1, = 1, = 0, = 1. In orr to stisy t oo circuit clus, w t = 1. In orr to stisy t oo circuit clus, w t = 1. In orr to stisy t ctiv clus, w t = 0. In orr to stisy t ulty circuit clus, w t = 0. In orr to stisy t ctiv clus, w t = 1. In orr to stisy t ulty circuit clus, w t = 0. In orr to stisy t oo circuit clus, w n itr =0, =0, or =0 n =0. In orr to stisy t oo circuit clus, w n itr =0, =0, or =0 n =0. Tror, w cn v t ollowin vctors to tst or t s--0 ult: : 000, 001, 010, 100, 101. ll obsrvbility is t t output, n. Rrncs Lrrb, Trcy. Tst Pttrn Gnrtion Usin ooln Stisibility IEEE Trnsctions on omputr-i Dsin, Jnury Sculz, M. H., Trisclr, E., n Srrt, T. M. SORTES: Hily Eicint utomtic Tst Pttrn Gnrtion Systm IEEE Trnsctions on omputr-i Dsin, Jnury P 7 o 7