Self-Checking Synchronous Sequential Circuit Design for ...

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

'HULYLQJ WKHVHOIFKHFNLQJV\QFKURQRXV VHTXHQWLDOFLUFXLWIURPDVWDWHWDEOH :H ZDQW WR REWDLQ D VHOIFKHFNLQJ V\QFKURQRXV VHTXHQWLDO FLUFXLW XQGHU WKH DVVXPSWLRQ WKDW WKH RXWSXW OLQHV RI LWV FRPELQDWLRQDO SDUW DUH FRQQHFWHG ZLWK WKH LQSXWOLQHVRIDFKHFNHU)LJ  [ [W

\ \V

& G GS

] ]S

&U

)LJ $6HOI&KHFNLQJV\QFKURQRXVFLUFXLW ZLWKDFKHFNHU

+HUH & LV WKH FRPELQDWLRQDOSDUWRI D VHTXHQWLDO FLUFXLW G  G S DUH WKH GHOD\ IOLSIORSV [  [ W  \   \ V  ]  ] S DUHWKHLQSXWRXWSXWDQGVWDWHYDUL

DEOHV

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 ^   W L `   5HSUHVHQW DQ\ FRGH ZRUG ZLWK WKH SURSHU ERROHDQ YHFWRU D RIWKHOHQJWKN  $GGWKHVDPH D IRUHDFKFXEH XL  XL 8 LY   ([HFXWHVWHSVIRUHYHU\8 L  L

^  _ 4_ ` 

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

YDOXHIRU X M 

3URSRVDO  $Q XQH[SDQGHG FXEH XL IURP )



GRHV QRW LQWHUVHFW ZLWK DQ H[SDQGHG FXEH X M UHVXOWHG

IURP X M SURYLGHG WKDW WKH RXWSXW FRGH ZRUGV RI WKH FXEHV XL  X M DUHGLIIHUHQW

3URRI ,I XL 8 LY  X M 8 LZ WKHQ ERROHDQ YHFWRUV

D L  D M WKDWZHUHVSHFWLYHO\DGGWR X L DQG X M DUHELGL

UHFWLRQDO&RQVHTXHQWO\ZKHQDQ\YDOXHFRPSRQHQWRI D M FKDQJHVIRUWKHV\PERO ZHREWDLQFXEH X D M WKDW LVDWOHDVWRUWKLJRQDOWR D L 

,I XL 8 LY  X M 8 MZ WKHQWKHVHFXEHVDUHELGLUHF

WLRQDODPRQJWKHVWDWHYDULDEOHV ]  ] S 4('

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

7KH JHQHUDO YLHZ RI D VHOIFKHFNLQJ V\QFKURQRXV VH TXHQWLDO FLUFXLW ZLWK WKH DGGLWLRQDO LQSXW DQG RXWSXW YDULDEOHVLVWKHIROORZLQJ)LJ +HUH [c  [ Uc DUHWKH DGGLWLRQDO LQSXW YDULDEOHV DQG \c  \ Dc  DUH WKH DGGL WLRQDORXWSXWYDULDEOHV \

[  [ U

[ [W

&

\V \  \ D

&U

] ]S

G GS

)LJ $6HOI&KHFNLQJV\QFKURQRXVVHTXHQWLDO FLUFXLWZLWKWKHDGGLWLRQDOLQSXWDQGRXWSXWOLQHV

([SHULPHQWDOGDWD

&RQVLGHUWKHH[DPSOHVKRZQLQ7DEOH:HKDYH WKHIROORZLQJ67*GHVFULSWLRQ [

         

[

         

[

         

T          

T          

\

         

\

         

7DEOH \

         

\

         

\

         

:H QHHG  VWDWH YDULDEOHV WR HQFRGH VWDWHV ZLWK WKHFRGHZRUGVRIWKHVDPHZHLJKW                 ,W LV QHFHVVDU\ WR XVH  DGGLWLRQDO RXWSXW YDULDEOHV \ 

\ WR HQFRGH WKH RXWSXW VWDWHV ZLWK WKH FRGH ZRUGV RI WKH VDPH ZHLJKW 0RUHRYHU ZH KDYH WR DGG RQH LQSXW YDULDEOH [  WR SURYLGH RUWKRJRQDOLW\$V D UHVXOWZH REWDLQWKHV\VWHP )  DVIROORZV [ [  [  [ 

                           

] ]  ]  ] 

                         

] ]  ]  ] 

         

7DEOH

\ \  \  \  \  \ \

         

'HULYHWKHV\VWHP) IURP )  HQXPHUDWLQJWKH IXQFWLRQV RI WKH FXEH FKDUDFWHULVWLFV E\ WKH VWDWH DQG RXWSXWYDULDEOHV:HKDYHWKHIROORZLQJV\VWHP [ [  [  [                             

] ]  ]  ]                           

7DEOH

]   \   \   \ ]   \   \   \ ]  \  \   \ ]  \   \   \ ]  \  \   \  ]  \   \   \ ]  \   \   \ ]  \   \   \ ]  \   \   \ ]  \   \   \ 

EHQFKPDUNV

,IZHZDQWWRREWDLQWKHXQDWHV\VWHPRIWKHFRP SOHWHO\ GHWHUPLQHG ERROHDQ IXQFWLRQV ZH QHHG  DGGL WLRQDO LQSXW YDULDEOHV LQVWHG RI  7KHQ )  LV WKH IROORZLQJ [ [  [  [  [ 

                           

] ]  ]  ] 

                         

] ]  ]  ] 

          

7DEOH

\ \  \  \  \  \ \

         

&KDQJLQJ YDOXH FRPSRQHQWV IRU V\PERO  DPRQJ DOO FXEHV ZH GHULYH WKH XQDWH FRPSOHWHO\ GHWHU PLQHGV\VWHP) 7DEOH WKDWDOORZVPXOWLOHYHOV\QWKH VLV [ [  [  [  [                       

] ]  ]  ]                     

)RU FHUWDLQ EHQFKPDUNV ZH FDOFXODWHG WKH QXP EHUVRILQSXWVZHQHHGWRHQFRGHLQSXWFXEHVIURP67*   XVLQJPRXWRIQ HQFRGLQJ>@RU H[WHQGLQJFXEHV WRSURYLGHRUWKRJRQDOLW\ DQGWKHGLIIHUHQFHEHWZHHQ WKHP7KHUHVXOWVDUHWKHIROORZLQJ

7DEOH

]   \   \   \ ]  \  \   \ ]  \   \   \ ]  \  \   \  ]  \   \   \ ]  \   \   \ ]  \   \   \ ]  \   \   \ 

7DNHLQWRDFFRXQWWKDWHYHQUHSHDWHGGXSOLFDWLRQ RIWKHVHTXHQWLDOFLUFXLWGRHVQRWHQVXUHPDQLIHVWDWLRQRI VLQJOH VWXFNDW IDXOWV DW WKH FRPPRQ LQSXW OLQHV RI WKH VHTXHQWLDOGXSOLFDWHVDVXQLGLUHFWLRQDOHUURUV 0DQLIHVWDWLRQRIVLQJOHVWXFNDWIDXOWVDWWKHLQSXW OLQHV RIVHOIFKHFNLQJV\QFKURQRXVVHTXHQWLDOFLUFXLWVLV RI SULPDU\ LPSRUWDQFH IRU WKH VHOIFKHFNLQJ )60 QHW ZRUNGHVLJQ

PF PDUN OLRQ GN H[ H[ V RSXV

PRXWRIQ HQFRGLQJ        

H[WHQGLQJ FXEHV        

7DEOH

GLIIHUHQFH        

7DEOHVKRZVWKDWWKHQXPEHUVRILQSXWYDULDEOHV IRU WKHVH PHWKRGV DUH SUDFWLFDOO\ WKH VDPH 7DNH LQWR DFFRXQW WKDW PRXWRIQ HQFRGLQJ>@ GHPDQGV DQ DGGL WLRQDOFLUFXLW & IRUHQFRGLQJLQSXWVDQG & KDVDOVRWR EHDVHOIFKHFNLQJRQH

&RQFOXVLRQ

7KH QRYHO WHFKQLTXH RI WKH VHOIFKHFNLQJ V\Q FKURQRXV VHTXHQWLDO FLUFXLW GHVLJQ IRU WKH H[WHQGHG VHW RI VWXFNDW IDXOWV LV VXJJHVWHG ,W JLYHV SRVVLELOLWLHV RI FUHDWLQJ WKH VHOIFKHFNLQJ V\QFKURQRXV )60 QHWZRUNV ZLWKVLQJOHVWXFNDWIDXOWVDWWKH)60SROHV

5HIHUHQFHV

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