combinational logic implementation implementations of two level logic

31
CSE 370 - Spring 1999 - Combinational Implementation - 1 &RPELQDWLRQDOORJLFLPSOHPHQWDWLRQ 7ZROHYHOORJLF LPSOHPHQWDWLRQVRIWZROHYHOORJLF 1$1’125 0XOWLOHYHOORJLF IDFWRUHGIRUPV DQGRULQYHUWJDWHV 7LPHEHKDYLRU JDWHGHOD\V KD]DUGV 5HJXODUORJLF PXOWLSOH[RUV GHFRGHUV 3$/3/$V 520V CSE 370 - Spring 1999 - Combinational Implementation - 2 ,PSOHPHQWDWLRQVRIWZROHYHOORJLF 6XPRISURGXFWV $1’JDWHVWRIRUPSURGXFWWHUPVPLQWHUPV 25JDWHWRIRUPVXP 3URGXFWRIVXPV 25JDWHVWRIRUPVXPWHUPVPD[WHUPV $1’JDWHVWRIRUPSURGXFW

Upload: others

Post on 09-Feb-2022

5 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 1

&RPELQDWLRQDO�ORJLF�LPSOHPHQWDWLRQ

❚ 7ZR�OHYHO�ORJLF❙ LPSOHPHQWDWLRQV�RI�WZR�OHYHO�ORJLF❙ 1$1'�125

❚ 0XOWL�OHYHO�ORJLF❙ IDFWRUHG�IRUPV❙ DQG�RU�LQYHUW�JDWHV

❚ 7LPH�EHKDYLRU❙ JDWH�GHOD\V❙ KD]DUGV

❚ 5HJXODU�ORJLF❙ PXOWLSOH[RUV❙ GHFRGHUV❙ 3$/�3/$V❙ 520V

CSE 370 - Spring 1999 - Combinational Implementation - 2

,PSOHPHQWDWLRQV�RI�WZR�OHYHO�ORJLF

❚ 6XP�RI�SURGXFWV❙ $1'�JDWHV�WR�IRUP�SURGXFW�WHUPV��PLQWHUPV�❙ 25�JDWH�WR�IRUP�VXP

❚ 3URGXFW�RI�VXPV❙ 25�JDWHV�WR�IRUP�VXP�WHUPV��PD[WHUPV�❙ $1'�JDWHV�WR�IRUP�SURGXFW

Page 2: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 3

7ZR�OHYHO�ORJLF�XVLQJ�1$1'�JDWHV

❚ 5HSODFH�PLQWHUP�$1'�JDWHV�ZLWK�1$1'�JDWHV

❚ 3ODFH�FRPSHQVDWLQJ�LQYHUVLRQ�DW�LQSXWV�RI�25�JDWH

CSE 370 - Spring 1999 - Combinational Implementation - 4

7ZR�OHYHO�ORJLF�XVLQJ�1$1'�JDWHV��FRQW·G�

❚ 25�JDWH�ZLWK�LQYHUWHG�LQSXWV�LV�D�1$1'�JDWH❙ GH�0RUJDQV� $���%� ��$���%�

❚ 7ZR�OHYHO�1$1'�1$1'�QHWZRUN❙ LQYHUWHG�LQSXWV�DUH�QRW�FRXQWHG❙ LQ�D�W\SLFDO�FLUFXLW��LQYHUVLRQ�LV�GRQH�RQFH�DQG�VLJQDO�GLVWULEXWHG

Page 3: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 5

7ZR�OHYHO�ORJLF�XVLQJ�125�JDWHV

❚ 5HSODFH�PD[WHUP�25�JDWHV�ZLWK�125�JDWHV

❚ 3ODFH�FRPSHQVDWLQJ�LQYHUVLRQ�DW�LQSXWV�RI�$1'�JDWH

CSE 370 - Spring 1999 - Combinational Implementation - 6

7ZR�OHYHO�ORJLF�XVLQJ�125�JDWHV��FRQW·G�

❚ $1'�JDWH�ZLWK�LQYHUWHG�LQSXWV�LV�D�125�JDWH❙ GH�0RUJDQV� $���%� ��$���%�

❚ 7ZR�OHYHO�125�125�QHWZRUN❙ LQYHUWHG�LQSXWV�DUH�QRW�FRXQWHG❙ LQ�D�W\SLFDO�FLUFXLW��LQYHUVLRQ�LV�GRQH�RQFH�DQG�VLJQDO�GLVWULEXWHG

Page 4: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 7

25

1$1' 1$1'

25 $1'

125 125

$1'

7ZR�OHYHO�ORJLF�XVLQJ�1$1'�DQG�125�JDWHV

❚ 1$1'�1$1'�DQG�125�125�QHWZRUNV❙ GH�0RUJDQV�ODZ� �$���%� ���$���% �$���%��� ���$���%❙ ZULWWHQ�GLIIHUHQWO\� �$���% ���$���%� �$���%���� ���$���%�

❚ ,Q�RWKHU�ZRUGV�±±❙ 25�LV�WKH�VDPH�DV�1$1'�ZLWK�FRPSOHPHQWHG�LQSXWV❙ $1'�LV�WKH�VDPH�DV�125�ZLWK�FRPSOHPHQWHG�LQSXWV❙ 1$1'�LV�WKH�VDPH�DV�25�ZLWK�FRPSOHPHQWHG�LQSXWV❙ 125�LV�WKH�VDPH�DV�$1'�ZLWK�FRPSOHPHQWHG�LQSXWV

CSE 370 - Spring 1999 - Combinational Implementation - 8

$

%

&

'

=

$

%

&

'

=

1$1'

1$1'

1$1'

&RQYHUVLRQ�EHWZHHQ�IRUPV

❚ &RQYHUW�IURP�QHWZRUNV�RI�$1'V�DQG�25V�WR�QHWZRUNV�RI�1$1'V�DQG�125V❙ LQWURGXFH�DSSURSULDWH�LQYHUVLRQV���EXEEOHV��

❚ (DFK�LQWURGXFHG��EXEEOH��PXVW�EH�PDWFKHG�E\�D�FRUUHVSRQGLQJ��EXEEOH�❙ FRQVHUYDWLRQ�RI�LQYHUVLRQV❙ GR�QRW�DOWHU�ORJLF�IXQFWLRQ

❚ ([DPSOH��$1'�25�WR�1$1'�1$1'

Page 5: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 9

=� �>��$�����%������&�����'���@

��� �>��$���%�������&���'���@

��� �>��$���%�����&���'���@

��� ����$�����%�������&����'���➼

&RQYHUVLRQ�EHWZHHQ�IRUPV��FRQW·G�

❚ ([DPSOH��YHULI\�HTXLYDOHQFH�RI�WZR�IRUPV

$

%

&

'

=

$

%

&

'

=

1$1'

1$1'

1$1'

CSE 370 - Spring 1999 - Combinational Implementation - 10

6WHS��FRQVHUYH�EXEEOHV�

6WHS��FRQVHUYH�EXEEOHV�

125

125

125

?$

?%

?&

?'

=

125

125$

%

&

'

=

&RQYHUVLRQ�EHWZHHQ�IRUPV��FRQW·G�

❚ ([DPSOH��PDS�$1'�25�QHWZRUN�WR�125�125�QHWZRUN

$

%

&

'

=

Page 6: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 11

=� �^��>��$���%�����&���'���@��`

��� �^������$���%�������&���'�������`

��� ��������$���%�����&���'�

��� ��������$�����%�������&�����'����➼

&RQYHUVLRQ�EHWZHHQ�IRUPV��FRQW·G�

❚ ([DPSOH��YHULI\�HTXLYDOHQFH�RI�WZR�IRUPV

$

%

&

'

=

125

125

125

?$

?%

?&

?'

=

CSE 370 - Spring 1999 - Combinational Implementation - 12

$%&

'(

)*

;

0XOWL�OHYHO�ORJLF

❚ [� �$�'�)�����$�(�)�����%�'�)�����%�(�)�����&�'�)�����&�(�)�����*❙ UHGXFHG�VXP�RI�SURGXFWV�IRUP�±�DOUHDG\�VLPSOLILHG❙ ��[���LQSXW�$1'�JDWHV�����[���LQSXW�25�JDWH��WKDW�PD\�QRW�HYHQ�H[LVW��❙ ���ZLUHV�����OLWHUDOV�SOXV���LQWHUQDO�ZLUHV�

❚ [� ��$���%���&���'���(��)�����*❙ IDFWRUHG�IRUP�±�QRW�ZULWWHQ�DV�WZR�OHYHO�6�R�3❙ ��[���LQSXW�25�JDWH����[���LQSXW�25�JDWHV����[���LQSXW�$1'�JDWH❙ ���ZLUHV����OLWHUDOV�SOXV���LQWHUQDO�ZLUHV�

Page 7: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 13

/HYHO�� /HYHO�� /HYHO�� /HYHO��

RULJLQDO$1'�25�QHWZRUN

$

&'

%

%?&

)

LQWURGXFWLRQ�DQGFRQVHUYDWLRQ�RI�

EXEEOHV$

&'

%

%?&

)

UHGUDZQ�LQ�WHUPVRI�FRQYHQWLRQDO1$1'�JDWHV $

&'

?%

%?&

)

&RQYHUVLRQ�RI�PXOWL�OHYHO�ORJLF�WR�1$1'�JDWHV

❚ )� �$��%���&�'����%�&

CSE 370 - Spring 1999 - Combinational Implementation - 14

/HYHO�� /HYHO�� /HYHO�� /HYHO��

$

&'

%

%?&

)RULJLQDO$1'�25�QHWZRUN

LQWURGXFWLRQ�DQGFRQVHUYDWLRQ�RI�

EXEEOHV $

&

'%

%

?&

)

UHGUDZQ�LQ�WHUPVRI�FRQYHQWLRQDO

125�JDWHV?$

?&?'

%

?%&

)

&RQYHUVLRQ�RI�PXOWL�OHYHO�ORJLF�WR�125V

❚ )� �$��%���&�'����%�&

Page 8: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 15

$

;

%&

'

)�D�

RULJLQDO�FLUFXLW

$

;

%&

'

)�E�

DGG�GRXEOH�EXEEOHV�DW�LQSXWV

?'

$

?;

%&

)�F�

GLVWULEXWH�EXEEOHVVRPH�PLVPDWFKHV

?'

$

;

%&

)?;

�G�

LQVHUW�LQYHUWHUV�WR�IL[�PLVPDWFKHV

&RQYHUVLRQ�EHWZHHQ�IRUPV

❚ ([DPSOH

CSE 370 - Spring 1999 - Combinational Implementation - 16

��[��$2,�JDWHV\PERO

��[��$2,�JDWHV\PERO

1$1' 1$1' ,QYHUW

SRVVLEOH�LPSOHPHQWDWLRQ

$%

&'

=

$1' 25 ,QYHUW

ORJLFDO�FRQFHSW

$%

&'

=

$1'�25�LQYHUW�JDWHV

❚ $2,�IXQFWLRQ���WKUHH�VWDJHV�RI�ORJLF�²��$1'��25��,QYHUW❙ PXOWLSOH�JDWHV��SDFNDJHG��DV�D�VLQJOH�FLUFXLW�EORFN

Page 9: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 17

� �

� �

$

%

$

%

$

%

)

&RQYHUVLRQ�WR�$2,�IRUPV

❚ *HQHUDO�SURFHGXUH�WR�SODFH�LQ�$2,�IRUP❙ FRPSXWH�WKH�FRPSOHPHQW�RI�WKH�IXQFWLRQ�LQ�VXP�RI�SURGXFWV�IRUP❙ E\�JURXSLQJ�WKH��V�LQ�WKH�.DUQDXJK�PDS

❚ ([DPSOH���;25�LPSOHPHQWDWLRQ���±±���$�[RU�%� �$�%�����$�%❙ $2,�IRUP� )� ��$�%�����$�%�

CSE 370 - Spring 1999 - Combinational Implementation - 18

each implemented in a single 2x2 AOI gate

([DPSOHV�RI�XVLQJ�$2,�JDWHV

❚ ([DPSOH�❙ )� �%�&���$�&���$�%❙ )� �$�%���$�&���%�&❙ ,PSOHPHQWHG�E\���LQSXW���VWDFN�$2,�JDWH

❙ )� ��$���%���$���&���%���&�❙ )� ��%���&���$���&���$���%�❙ ,PSOHPHQWHG�E\���LQSXW���VWDFN�2$,�JDWH

❚ ([DPSOH����ELW�HTXDOLW\�IXQFWLRQ❙ =� ��$��%����$��%���$��%����$��%���$��%����$��%���$��%����$��%��

� �

� �

� �

� �&

%

$

Page 10: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 19

KLJK�LI�$��≠�%�ORZ���LI�$�� �%�

LI�DOO�LQSXWV�DUH�ORZ������WKHQ�$L� �%L��L �������RXWSXW�=�LV�KLJK

FRQVHUYDWLRQ�RI�EXEEOHV

$�%�

$�%�

$�%�

$�%�

125 =

([DPSOHV�RI�XVLQJ�$2,�JDWHV��FRQW·G�

❚ ([DPSOH���$2,�LPSOHPHQWDWLRQ�RI���ELW�HTXDOLW\�IXQFWLRQ

CSE 370 - Spring 1999 - Combinational Implementation - 20

6XPPDU\�IRU�PXOWL�OHYHO�ORJLF

❚ $GYDQWDJHV❙ FLUFXLWV�PD\�EH�VPDOOHU❙ JDWHV�KDYH�VPDOOHU�IDQ�LQ❙ FLUFXLWV�PD\�EH�IDVWHU

❚ 'LVDGYDQWDJHV❙ PRUH�GLIILFXOW�WR�GHVLJQ❙ WRROV�IRU�RSWLPL]DWLRQ�DUH�QRW�DV�JRRG�DV�IRU�WZR�OHYHO❙ DQDO\VLV�LV�PRUH�FRPSOH[

Page 11: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 21

7LPH�EHKDYLRU�RI�FRPELQDWLRQDO�QHWZRUNV

❚ :DYHIRUPV❙ YLVXDOL]DWLRQ�RI�YDOXHV�FDUULHG�RQ�VLJQDO�ZLUHV�RYHU�WLPH❙ XVHIXO�LQ�H[SODLQLQJ�VHTXHQFHV�RI�HYHQWV��FKDQJHV�LQ�YDOXH�

❚ 6LPXODWLRQ�WRROV�DUH�XVHG�WR�FUHDWH�WKHVH�ZDYHIRUPV❙ LQSXW�WR�WKH�VLPXODWRU�LQFOXGHV�JDWHV�DQG�WKHLU�FRQQHFWLRQV❙ LQSXW�VWLPXOXV��WKDW�LV��LQSXW�VLJQDO�ZDYHIRUPV

❚ 6RPH�WHUPV❙ JDWH�GHOD\�²�WLPH�IRU�FKDQJH�DW�LQSXW�WR�FDXVH�FKDQJH�DW�RXWSXW

❘ PLQ�GHOD\�±�W\SLFDO�QRPLQDO�GHOD\�±�PD[�GHOD\❘ FDUHIXO�GHVLJQHUV�GHVLJQ�IRU�WKH�ZRUVW�FDVH

❙ ULVH�WLPH�²�WLPH�IRU�RXWSXW�WR�WUDQVLWLRQ�IURP�ORZ�WR�KLJK�YROWDJH❙ IDOO�WLPH�²�WLPH�IRU�RXWSXW�WR�WUDQVLWLRQ�IURP�KLJK�WR�ORZ�YROWDJH❙ SXOVH�ZLGWK�²�WLPH�WKDW�DQ�RXWSXW�VWD\V�KLJK�RU�VWD\V�ORZ�EHWZHHQ�FKDQJHV

CSE 370 - Spring 1999 - Combinational Implementation - 22

)�LV�QRW�DOZD\V��

SXOVH���JDWH�GHOD\V�ZLGH

'�UHPDLQV�KLJK�IRUWKUHH�JDWH�GHOD\V�DIWHU

$�FKDQJHV�IURP�ORZ�WR�KLJK

)$ % & '

0RPHQWDU\�FKDQJHV�LQ�RXWSXWV

❚ &DQ�EH�XVHIXO�²�SXOVH�VKDSLQJ�FLUFXLWV

❚ &DQ�EH�D�SUREOHP�²�LQFRUUHFW�FLUFXLW�RSHUDWLRQ��JOLWFKHV�KD]DUGV�

❚ ([DPSOH��SXOVH�VKDSLQJ�FLUFXLW❙ $���$� ��❙ GHOD\V�PDWWHU�LQ�IXQFWLRQ

Page 12: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 23

LQLWLDOO\�

XQGHILQHG

FORVH�VZLWFK

RSHQ�VZLWFK

RSHQ�VZLWFK

UHVLVWRU

$ %

&'

2VFLOODWRU\�EHKDYLRU

❚ $QRWKHU�SXOVH�VKDSLQJ�FLUFXLW

CSE 370 - Spring 1999 - Combinational Implementation - 24

+D]DUGV�JOLWFKHV

❚ +D]DUGV�JOLWFKHV��XQZDQWHG�VZLWFKLQJ�DW�WKH�RXWSXWV❙ RFFXU�ZKHQ�GLIIHUHQW�SDWKV�WKURXJK�FLUFXLW�KDYH�GLIIHUHQW�SURSDJDWLRQ�GHOD\V

❘ DV�LQ�SXOVH�VKDSLQJ�FLUFXLWV�ZH�MXVW�DQDO\]HG❙ GDQJHURXV�LI�ORJLF�FDXVHV�DQ�DFWLRQ�ZKLOH�RXWSXW�LV�XQVWDEOH

❘ PD\�QHHG�WR�JXDUDQWHH�DEVHQFH�RI�JOLWFKHV

❚ 8VXDO�VROXWLRQV❙ ���ZDLW�XQWLO�VLJQDOV�DUH�VWDEOH��E\�XVLQJ�D�FORFN�

SUHIHUDEOH��HDVLHVW�WR�GHVLJQ�ZKHQ�WKHUH�LV�D�FORFN�±�V\QFKURQRXV�GHVLJQ�❙ ���GHVLJQ�KD]DUG�IUHH�FLUFXLWV

VRPHWLPHV�QHFHVVDU\��FORFN�QRW�XVHG�±�DV\QFKURQRXV�GHVLJQ�

Page 13: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 25

�� �

� �� �

� �� �

�� �

7\SHV�RI�KD]DUGV

❚ 6WDWLF���KD]DUG❙ LQSXW�FKDQJH�FDXVHV�RXWSXW�WR�JR�IURP���WR���WR��

❚ 6WDWLF���KD]DUG❙ LQSXW�FKDQJH�FDXVHV�RXWSXW�WR�JR�IURP���WR���WR��

❚ '\QDPLF�KD]DUGV❙ LQSXW�FKDQJH�FDXVHV�D�GRXEOH�FKDQJHIURP���WR���WR���WR���25�IURP���WR���WR���WR��

CSE 370 - Spring 1999 - Combinational Implementation - 26

)

$

%

6

6

)

KD]DUG

VWDWLF���KD]DUG VWDWLF���KD]DUG

$6

%

6

6WDWLF�KD]DUGV

❚ 'XH�WR�D�OLWHUDO�DQG�LWV�FRPSOHPHQW�PRPHQWDULO\�WDNLQJ�RQ�WKH�VDPH�YDOXH❙ WKURXJK�GLIIHUHQW�SDWKV�ZLWK�GLIIHUHQW�GHOD\V�DQG�UHFRQYHUJLQJ

❚ 0D\�FDXVH�DQ�RXWSXW�WKDW�VKRXOG�KDYH�VWD\HG�DW�WKH�VDPH�YDOXHWR�PRPHQWDULO\�WDNH�RQ�WKH�ZURQJ�YDOXH

❚ ([DPSOH��PXOWLSOH[HU

Page 14: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 27

%�

$

&

%�

)

KD]DUG

G\QDPLF�KD]DUGV

%�

$

&

%

)

��

'\QDPLF�KD]DUGV

❚ 'XH�WR�WKH�VDPH�YHUVLRQV�RI�D�OLWHUDO�WDNLQJ�RQ�RSSRVLWH�YDOXHV❙ WKURXJK�GLIIHUHQW�SDWKV�ZLWK�GLIIHUHQW�GHOD\V�DQG�UHFRQYHUJLQJ

❚ 0D\�FDXVH�DQ�RXWSXW�WKDW�ZDV�WR�FKDQJH�YDOXHWR�FKDQJH���WLPHV�LQVWHDG�RI�RQFH

❚ ([DPSOH�

CSE 370 - Spring 1999 - Combinational Implementation - 28

PXOWLSOH[HU GHPXOWLSOH[HU �[��VZLWFK

FRQWURO FRQWURO

0DNLQJ�FRQQHFWLRQV

❚ 'LUHFW�SRLQW�WR�SRLQW�FRQQHFWLRQV�EHWZHHQ�JDWHV❙ ZLUHV�ZHYH�VHHQ�VR�IDU

❚ 5RXWH�RQH�RI�PDQ\�LQSXWV�WR�D�VLQJOH�RXWSXW�����PXOWLSOH[HU

❚ 5RXWH�D�VLQJOH�LQSXW�WR�RQH�RI�PDQ\�RXWSXWV�����GHPXOWLSOH[HU

Page 15: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 29

0X[�DQG�GHPX[

❚ 6ZLWFK�LPSOHPHQWDWLRQ�RI�PXOWLSOH[HUV�DQG�GHPXOWLSOH[HUV❙ FDQ�EH�FRPSRVHG�WR�PDNH�DUELWUDU\�VL]H�VZLWFKLQJ�QHWZRUNV❙ XVHG�WR�LPSOHPHQW�PXOWLSOH�VRXUFH�PXOWLSOH�GHVWLQDWLRQ�LQWHUFRQQHFWLRQV

$

%

<

=

$

%

<

=

CSE 370 - Spring 1999 - Combinational Implementation - 30

PXOWLSOH�LQSXW�VRXUFHV

PXOWLSOH�RXWSXW�GHVWLQDWLRQV

08;

$ %

6XP

6D

6V

6E

%�

08;

'(08;

0X[�DQG�GHPX[��FRQWG�

❚ 8VHV�RI�PXOWLSOH[HUV�GHPXOWLSOH[HUV�LQ�PXOWL�SRLQW�FRQQHFWLRQV

%�$� $�

6� 6�

Page 16: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 31

WZR�DOWHUQDWLYH�IRUPVIRU�D�����0X[�WUXWK�WDEOH

IXQFWLRQDO�IRUP

ORJLFDO�IRUP

$ =

� ,�� ,�

,� ,� $ =

� � � �

� � � �

� � � �

� � � �

� � � �

� � � �

� � � �

� � � �

=� �$�,�����$�,�

0XOWLSOH[HUV�VHOHFWRUV

❚ 0XOWLSOH[HUV�VHOHFWRUV��JHQHUDO�FRQFHSW❙ �Q�GDWD�LQSXWV��Q�FRQWURO�LQSXWV��FDOOHG��VHOHFWV������RXWSXW❙ XVHG�WR�FRQQHFW��Q�SRLQWV�WR�D�VLQJOH�SRLQW❙ FRQWURO�VLJQDO�SDWWHUQ�IRUPV�ELQDU\�LQGH[�RI�LQSXW�FRQQHFWHG�WR�RXWSXW

CSE 370 - Spring 1999 - Combinational Implementation - 32

������

,�,�,�,�,�,�,�,�

$��%��&

���PX[

=

,�,�,�,�

$��%

���PX[

=,�,�

$

���PX[

=

N �

Q

0XOWLSOH[HUV�VHOHFWRUV��FRQWG�

❚ ����PX[� =� �$�,����$�,�

❚ ����PX[� =� �$�%�,����$�%�,����$�%�,����$�%�,�

❚ ����PX[� =� �$�%�&�,����$�%�&�,����$�%�&�,����$�%�&�,����������$�%�&�,����$�%�&�,�����$�%�&�,�����$�%�&�,�

❚ ,Q�JHQHUDO��=� �Σ���������PN,N�

❙ LQ�PLQWHUP�VKRUWKDQG�IRUP�IRU�D��Q���0X[

Page 17: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 33

*DWH�OHYHO�LPSOHPHQWDWLRQ�RI�PX[HV

❚ ����PX[

❚ ����PX[

CSE 370 - Spring 1999 - Combinational Implementation - 34

FRQWURO�VLJQDOV�%�DQG�&�VLPXOWDQHRXVO\�FKRRVH�RQH�RI�,���,���,���,��DQG�RQH�RI�,���,���,���,�

FRQWURO�VLJQDO�$�FKRRVHV�ZKLFK�RI�WKHXSSHU�RU�ORZHU�PX[V�RXWSXW�WR�JDWH�WR�=

DOWHUQDWLYH

LPSOHPHQWDWLRQ

&

=

$��%

���PX[

���PX[

���PX[

���PX[

���PX[

,�,�

,�,�

,�,�

,�,�

���PX[

&DVFDGLQJ�PXOWLSOH[HUV

❚ /DUJH�PXOWLSOH[HUV�FDQ�EH�LPSOHPHQWHG�E\�FDVFDGLQJ�VPDOOHU�RQHV

=

,�,�,�,�

$

,�,�,�,�

%��&

���PX[

���PX[

���PX[

���PX[

Page 18: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 35CA B

01234567

10100011

S2

8:1 MUX

S1 S0

F

0XOWLSOH[HUV�DV�JHQHUDO�SXUSRVH�ORJLF

❚ $��Q���PXOWLSOH[HU�FDQ�LPSOHPHQW�DQ\�IXQFWLRQ�RI�Q�YDULDEOHV❙ ZLWK�WKH�YDULDEOHV�XVHG�DV�FRQWURO�LQSXWV�DQG❙ WKH�GDWD�LQSXWV�WLHG�WR���RU��❙ LQ�HVVHQFH��D�ORRNXS�WDEOH

❚ ([DPSOH�❙ )�$�%�&�� �P����P����P����P�������������� �$%&���$%&���$%&���$%&������������� �$%�&����$%�&����$%������$%���

CSE 370 - Spring 1999 - Combinational Implementation - 36

A B C F0 0 0 10 0 1 00 1 0 10 1 1 01 0 0 01 0 1 01 1 0 11 1 1 1

C’

C’

0

1 A B

S1 S0

F0123

4:1 MUX

C’C’01

F

CA B

01234567

10100011

S2

8:1 MUX

S1 S0

0XOWLSOH[HUV�DV�JHQHUDO�SXUSRVH�ORJLF��FRQW·G�

❚ $��Q�����PXOWLSOH[HU�FDQ�LPSOHPHQW�DQ\�IXQFWLRQ�RI�Q�YDULDEOHV❙ ZLWK�Q���YDULDEOHV�XVHG�DV�FRQWURO�LQSXWV�DQG❙ WKH�GDWD�LQSXWV�WLHG�WR�WKH�ODVW�YDULDEOH�RU�LWV�FRPSOHPHQW

❚ ([DPSOH�❙ )�$�%�&�� �P����P����P����P�������������� �$%&���$%&���$%&���$%&������������� �$%�&����$%�&����$%������$%���

Page 19: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 37

Q���PX[�FRQWURO�YDULDEOHV

VLQJOH�PX[�GDWD�YDULDEOH

IRXU�SRVVLEOHFRQILJXUDWLRQVRI�WUXWK�WDEOH�URZVFDQ�EH�H[SUHVVHGDV�D�IXQFWLRQ�RI�,Q

FKRRVH�$�%�&�DV�FRQWURO�YDULDEOHV

PXOWLSOH[HU�LPSOHPHQWDWLRQ

,� ,� ����� ,Q�� ,Q ��)

� � � � � � � � �

� � � � � � � � �

� ,Q ,Q �

0XOWLSOH[HUV�DV�JHQHUDO�SXUSRVH�ORJLF��FRQW·G�

❚ *HQHUDOL]DWLRQ

❚ ([DPSOH��)�$�%�&�'��FDQ�EH�LPSOHPHQWHG�E\�DQ�����08;

CA B

01234567

1D01D’DD’D’

S2

8:1 MUX

S1 S0

� �

� �

� �

� �'

$

� �

� �

� �

� �

%

&

CSE 370 - Spring 1999 - Combinational Implementation - 38

����'HFRGHU�2�� �*�•��6¶2�� �*�•��6�

��������'HFRGHU�����2�� �*�•��6�¶�•��6�¶2�� �*�•��6�¶�•��6�2�� �*�•��6���•��6�¶2�� �*�•��6���•��6�

������������'HFRGHU�����������2�� �*�•��6�¶�•��6�¶�•�6�¶2�� �*�•��6�¶�•��6�¶�•�6�2�� �*�•��6�¶�•��6���•�6�¶2�� �*�•��6�¶�•��6���•�6�2�� �*�•��6���•��6�¶�•�6�¶2�� �*�•��6���•��6�¶�•�6�2�� �*�•��6���•��6���•�6�¶2�� �*�•��6���•��6���•�6�

'HPXOWLSOH[HUV�GHFRGHUV

❚ 'HFRGHUV�GHPXOWLSOH[HUV��JHQHUDO�FRQFHSW❙ VLQJOH�GDWD�LQSXW��Q�FRQWURO�LQSXWV���Q��RXWSXWV❙ FRQWURO�LQSXWV��FDOOHG�³VHOHFWV´��6���UHSUHVHQW�ELQDU\�LQGH[�RI�RXWSXW�WRZKLFK�WKH�LQSXW�LV�FRQQHFWHG

❙ GDWD�LQSXW�XVXDOO\�FDOOHG�³HQDEOH´��*�

Page 20: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 39

DFWLYH�KLJK�HQDEOH

DFWLYH�ORZ�HQDEOH

DFWLYH�KLJK�HQDEOH

DFWLYH�ORZ�HQDEOH

2�*

6

2�

2�?*

6

2�

6�

2�

2�

2�*

2�

6� 6�

2�

2�

2�?*

2�

6�

*DWH�OHYHO�LPSOHPHQWDWLRQ�RI�GHPXOWLSOH[HUV

❚ ����GHFRGHUV

❚ ����GHFRGHUV

CSE 370 - Spring 1999 - Combinational Implementation - 40

GHPXOWLSOH[HU�JHQHUDWHV�DSSURSULDWHPLQWHUP�EDVHG�RQ�FRQWURO�VLJQDOV�LW��GHFRGHV��FRQWURO�VLJQDOV�

'HPXOWLSOH[HUV�DV�JHQHUDO�SXUSRVH�ORJLF

❚ $�Q��Q�GHFRGHU�FDQ�LPSOHPHQW�DQ\�IXQFWLRQ�RI�Q�YDULDEOHV❙ ZLWK�WKH�YDULDEOHV�XVHG�DV�FRQWURO�LQSXWV❙ WKH�HQDEOH�LQSXWV�WLHG�WR���DQG❙ WKH�DSSURSULDWH�PLQWHUPV�VXPPHG�WR�IRUP�WKH�IXQFWLRQ

$%&$%&$%&$%&$%&$%&$%&$%&

&$ %

��������

6�

����'(&

6� 6�

³�´

Page 21: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 41

)�

)�

)�

'HPXOWLSOH[HUV�DV�JHQHUDO�SXUSRVH�ORJLF��FRQW·G�

❚ )�� �$�%�&�'���$�%�&�'���$�%�&�'

❚ )�� �$�%�&�'¶���$�%�&

❚ )�� ��$���%���&���'�

$ %

� $%&'� $%&'� $%&'� $%&'� $%&'� $%&'� $%&'� $%&'� $%&'� $%&'�� $%&'�� $%&'�� $%&'�� $%&'�� $%&'�� $%&'

����'(&(QDEOH

& '

CSE 370 - Spring 1999 - Combinational Implementation - 42

� $%&'(�������

6�

����'(&

6� 6�

$ %

����6�

����'(&

6�

)

��� $%&'(�����

6�

����'(&

6� 6�

(& '

� $%&'(������� $%&'(

&DVFDGLQJ�GHFRGHUV

❚ �����GHFRGHU❙ �[����GHFRGHU❙ �[����GHFRGHUV

����'(&

�������� $%&'(

(& '

6� 6� 6� 6�

����'(&

6� 6�

Page 22: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 43

���������

LQSXWV

$1'

DUUD\

���������

RXWSXWV

25

DUUD\SURGXFW

WHUPV

3URJUDPPDEOH�ORJLF�DUUD\V

❚ 3UH�IDEULFDWHG�EXLOGLQJ�EORFN�RI�PDQ\�$1'�25�JDWHV❙ DFWXDOO\�125�RU�1$1'❙ �SHUVRQDOL]HG��E\�PDNLQJ�RU�EUHDNLQJ�FRQQHFWLRQV�DPRQJ�WKH�JDWHV❙ SURJUDPPDEOH�DUUD\�EORFN�GLDJUDP�IRU�VXP�RI�SURGXFWV�IRUP

CSE 370 - Spring 1999 - Combinational Implementation - 44

H[DPSOH�

)�� �$����%�&)�� �$�&�����$�%)�� �%�&�����$�%)�� �%�&�����$

SHUVRQDOLW\�PDWUL[�� �XQFRPSOHPHQWHG�LQ�WHUP�� �FRPSOHPHQWHG�LQ�WHUP±� �GRHV�QRW�SDUWLFLSDWH

�� �WHUP�FRQQHFWHG�WR�RXWSXW�� �QR�FRQQHFWLRQ�WR�RXWSXW

LQSXW�VLGH�

RXWSXW�VLGH�

SURGXFW LQSXWV RXWSXWV

WHUP $ % & )� )� )� )�

$% � � ± � � � �

%& ± � � � � � �

$& � ± � � � � �

%& ± � � � � � �

$ � ± ± � � � �UHXVH�RI�WHUPV

(QDEOLQJ�FRQFHSW

❚ 6KDUHG�SURGXFW�WHUPV�DPRQJ�RXWSXWV

Page 23: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 45

%HIRUH�SURJUDPPLQJ

❚ $OO�SRVVLEOH�FRQQHFWLRQV�DUH�DYDLODEOH�EHIRUH��SURJUDPPLQJ�❙ LQ�UHDOLW\��DOO�$1'�DQG�25�JDWHV�DUH�1$1'V

CSE 370 - Spring 1999 - Combinational Implementation - 46

$ % &

)� )� )�)�

$%

%&

$&

%&

$

$IWHU�SURJUDPPLQJ

❚ 8QZDQWHG�FRQQHFWLRQV�DUH��EORZQ�❙ IXVH��QRUPDOO\�FRQQHFWHG��EUHDN�XQZDQWHG�RQHV�❙ DQWL�IXVH��QRUPDOO\�GLVFRQQHFWHG��PDNH�ZDQWHG�FRQQHFWLRQV�

Page 24: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 47

QRWDWLRQ�IRU�LPSOHPHQWLQJ

)�� �$�%�����$�%

)�� �&�'�����&�'

$%�$%&'�&'

$%

$%

&'

&'

$ % & '

$OWHUQDWH�UHSUHVHQWDWLRQ�IRU�KLJK�IDQ�LQ�VWUXFWXUHV

❚ 6KRUW�KDQG�QRWDWLRQ�VR�ZH�GRQW�KDYH�WR�GUDZ�DOO�WKH�ZLUHV❙ ���VLJQLILHV�D�FRQQHFWLRQ�LV�SUHVHQW�DQG�SHUSHQGLFXODU�VLJQDO�LV�DQ�LQSXWWR�JDWH

CSE 370 - Spring 1999 - Combinational Implementation - 48

$ % & )� )� )� )� )� )�� � � � � � � � �� � � � � � � � �� � � � � � � � �� � � � � � � � �� � � � � � � � �� � � � � � � � �� � � � � � � � �� � � � � � � � �

$%&

$%&

$%&

$%&

$%&

$%&

$%&

$%&

$ % &

)� )� )� )� )�)�

IXOO�GHFRGHU�DV�IRU�PHPRU\�DGGUHVV

ELWV�VWRUHG�LQ�PHPRU\

3URJUDPPDEOH�ORJLF�DUUD\�H[DPSOH

❚ 0XOWLSOH�IXQFWLRQV�RI�$��%��&❙ )�� �$�%�&❙ )�� �$���%���&❙ )�� �$�%�&❙ )�� �$���%���&❙ )�� �$�[RU�%�[RU�&❙ )�� �$�[QRU�%�[QRU�&

Page 25: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 49

D�JLYHQ�FROXPQ�RI�WKH�25�DUUD\�KDV�DFFHVV�WR�RQO\�D�VXEVHW�RI�WKH�SRVVLEOH�SURGXFW�WHUPV

3$/V�DQG�3/$V

❚ 3URJUDPPDEOH�ORJLF�DUUD\��3/$�❙ ZKDW�ZHYH�VHHQ�VR�IDU❙ XQFRQVWUDLQHG�IXOO\�JHQHUDO�$1'�DQG�25�DUUD\V

❚ 3URJUDPPDEOH�DUUD\�ORJLF��3$/�❙ FRQVWUDLQHG�WRSRORJ\�RI�WKH�25�DUUD\❙ LQQRYDWLRQ�E\�0RQROLWKLF�0HPRULHV❙ IDVWHU�DQG�VPDOOHU�25�SODQH

CSE 370 - Spring 1999 - Combinational Implementation - 50

����������;�����

����������;������

����������;����;

����������;����;�

'

$

%

&

PLQLPL]HG�IXQFWLRQV�

:� �$���%�'���%�&;� �%�&<� �%���&=� �$%&'���%�&�'���$�'���%�&�'

$ % & ' : ; < =� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � � � � � �� � � ± ± ± ± ±� � ± ± ± ± ± ±

����������;�����

����������;������

����������;����;

����������;����;�

'

$

%

&

.�PDS�IRU�: .�PDS�IRU�;

����������;�����

����������;������

����������;����;

����������;����;�

'

$

%

&

.�PDS�IRU�<

3$/V�DQG�3/$V��GHVLJQ�H[DPSOH

❚ %&'�WR�*UD\�FRGH�FRQYHUWHU

.�PDS�IRU�=

����������;�����

����������;������

����������;����;

����������;����;�

'

$

%

&

Page 26: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 51

QRW�D�SDUWLFXODUO\�JRRGFDQGLGDWH�IRU�3$/�3/$

LPSOHPHQWDWLRQ�VLQFH�QR�WHUPV�DUH�VKDUHG�DPRQJ�RXWSXWV

KRZHYHU��PXFK�PRUH�FRPSDFW�DQG�UHJXODU�LPSOHPHQWDWLRQ�ZKHQ�FRPSDUHG�ZLWK�GLVFUHWH�

$1'�DQG�25�JDWHV

$ %� & '

: ;� < =

$

%'

%&

%&

%

&

$%&'

%&'

$'

%&'

PLQLPL]HG�IXQFWLRQV�

:� �$���%�'���%�&;� �%�&<� �%���&=� �$%&'���%�&�'���$�'���%�&�'

3$/V�DQG�3/$V��GHVLJQ�H[DPSOH��FRQW·G�

❚ &RGH�FRQYHUWHU��SURJUDPPHG�3/$

CSE 370 - Spring 1999 - Combinational Implementation - 52

��SURGXFW�WHUPV�

SHU�HDFK�25�JDWH

$

%'

%&

%&

%

&

$%&'

%&'

$'

%&'

: ; < =

$ %� & '

3$/V�DQG�3/$V��GHVLJQ�H[DPSOH��FRQW·G�

❚ &RGH�FRQYHUWHU��SURJUDPPHG�3$/

Page 27: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 53

:

;

<

=

%

%

%

%

%

%

?%&

&

&

&

&$

$$

'

'

'

?'

?'

3$/V�DQG�3/$V��GHVLJQ�H[DPSOH��FRQW·G�

❚ &RGH�FRQYHUWHU��1$1'�JDWH�LPSOHPHQWDWLRQ❙ ORVV�RU�UHJXODULW\��KDUGHU�WR�XQGHUVWDQG❙ KDUGHU�WR�PDNH�FKDQJHV

CSE 370 - Spring 1999 - Combinational Implementation - 54(4 1( /7 *7

$%&'

$%&'

$%&'

$%&'

$&

$&

%'

%'

$%'

%&'

$%&

%&'

$ % & '

3$/V�DQG�3/$V��DQRWKHU�GHVLJQ�H[DPSOH

❚ 0DJQLWXGH�FRPSDUDWRU

����������������

�����������������

����������������

�����������������

'

$

%

&

����������������

�����������������

����������������

�����������������

'

$

%

&

����������������

�����������������

����������������

�����������������

'

$

%

&

����������������

�����������������

����������������

�����������������

'

$

%

&

.�PDS�IRU�(4 .�PDS�IRU�1(

.�PDS�IRU�*7.�PDS�IRU�/7

Page 28: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 55

GHFRGHU

� Q��

$GGUHVV

������Q

� � � �

ZRUG>L@� �����

ZRUG>M@� �����

ELW�OLQHV��QRUPDOO\�SXOOHG�WR���WKURXJK�UHVLVWRU�±�VHOHFWLYHO\�FRQQHFWHG�WR���E\�ZRUG�OLQH�FRQWUROOHG�VZLWFKHV�

M

L

LQWHUQDO�RUJDQL]DWLRQ

ZRUG�OLQHV��RQO\�RQH�LV�DFWLYH�±�GHFRGHU�LV�MXVW�ULJKW�IRU�WKLV�

5HDG�RQO\�PHPRULHV

❚ 7ZR�GLPHQVLRQDO�DUUD\�RI��V�DQG��V❙ HQWU\��URZ��LV�FDOOHG�D��ZRUG�❙ ZLGWK�RI�URZ� �ZRUG�VL]H❙ LQGH[�LV�FDOOHG�DQ��DGGUHVV�❙ DGGUHVV�LV�LQSXW❙ VHOHFWHG�ZRUG�LV�RXWSXW

CSE 370 - Spring 1999 - Combinational Implementation - 56

)�� �$�%�&�����$�%�&�����$�%�&

)�� �$�%�&�����$�%�&�����$�%�&

)�� �$�%�&�����$�%�&�����$�%�&

)�� �$�%�&�����$�%�&����$�%�&

WUXWK�WDEOH

$ % & )� )� )� )�� � � � � � �� � � � � � �� � � � � � �� � � � � � �� � � � � � �� � � � � � �� � � � � � �� � � � � � �

EORFN�GLDJUDP

520��ZRUGV�[���ELWV�ZRUG

DGGUHVV RXWSXWV$ % & )�)�)�)�

520V�DQG�FRPELQDWLRQDO�ORJLF

❚ &RPELQDWLRQDO�ORJLF�LPSOHPHQWDWLRQ��WZR�OHYHO�FDQRQLFDO�IRUP��XVLQJ�D�520

Page 29: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 57

520�VWUXFWXUH

❚ 6LPLODU�WR�D�3/$�VWUXFWXUH�EXW�ZLWK�D�IXOO\�GHFRGHG�$1'�DUUD\❙ FRPSOHWHO\�IOH[LEOH�25�DUUD\��XQOLNH�3$/�

Q�DGGUHVV�OLQHV

���������

LQSXWV

GHFRGHU �Q�ZRUG

OLQHV

���������

RXWSXWV

memoryarray

(2n wordsby m bits)

P�GDWD�OLQHV

CSE 370 - Spring 1999 - Combinational Implementation - 58

520�YV��3/$

❚ 520�DSSURDFK�DGYDQWDJHRXV�ZKHQ❙ GHVLJQ�WLPH�LV�VKRUW��QR�QHHG�WR�PLQLPL]H�RXWSXW�IXQFWLRQV�❙ PRVW�LQSXW�FRPELQDWLRQV�DUH�QHHGHG��H�J���FRGH�FRQYHUWHUV�❙ OLWWOH�VKDULQJ�RI�SURGXFW�WHUPV�DPRQJ�RXWSXW�IXQFWLRQV

❚ 520�SUREOHPV❙ VL]H�GRXEOHV�IRU�HDFK�DGGLWLRQDO�LQSXW❙ FDQW�H[SORLW�GRQW�FDUHV

❚ 3/$�DSSURDFK�DGYDQWDJHRXV�ZKHQ❙ GHVLJQ�WRROV�DUH�DYDLODEOH�IRU�PXOWL�RXWSXW�PLQLPL]DWLRQ❙ WKHUH�DUH�UHODWLYHO\�IHZ�XQLTXH�PLQWHUP�FRPELQDWLRQV❙ PDQ\�PLQWHUPV�DUH�VKDUHG�DPRQJ�WKH�RXWSXW�IXQFWLRQV

❚ 3$/�SUREOHPV❙ FRQVWUDLQHG�IDQ�LQV�RQ�25�SODQH

Page 30: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 59

5HJXODU�ORJLF�VWUXFWXUHV�IRU�WZR�OHYHO�ORJLF

❚ 520�±�IXOO�$1'�SODQH��JHQHUDO�25�SODQH❙ FKHDS��KLJK�YROXPH�FRPSRQHQW�❙ FDQ�LPSOHPHQW�DQ\�IXQFWLRQ�RI�Q�LQSXWV❙ PHGLXP�VSHHG

❚ 3$/�±�SURJUDPPDEOH�$1'�SODQH��IL[HG�25�SODQH❙ LQWHUPHGLDWH�FRVW❙ FDQ�LPSOHPHQW�IXQFWLRQV�OLPLWHG�E\�QXPEHU�RI�WHUPV❙ KLJK�VSHHG��RQO\�RQH�SURJUDPPDEOH�SODQH�WKDW�LV�PXFK�VPDOOHU�WKDQ520V�GHFRGHU�

❚ 3/$�±�SURJUDPPDEOH�$1'�DQG�25�SODQHV❙ PRVW�H[SHQVLYH��PRVW�FRPSOH[�LQ�GHVLJQ��QHHG�PRUH�VRSKLVWLFDWHG�WRROV�❙ FDQ�LPSOHPHQW�DQ\�IXQFWLRQ�XS�WR�D�SURGXFW�WHUP�OLPLW❙ VORZ��WZR�SURJUDPPDEOH�SODQHV�

CSE 370 - Spring 1999 - Combinational Implementation - 60

5HJXODU�ORJLF�VWUXFWXUHV�IRU�PXOWL�OHYHO�ORJLF

❚ 'LIILFXOW�WR�GHYLVH�D�UHJXODU�VWUXFWXUH�IRU�DUELWUDU\�FRQQHFWLRQV�EHWZHHQ�DODUJH�VHW�RI�GLIIHUHQW�W\SHV�RI�JDWHV❙ HIILFLHQF\�VSHHG�FRQFHUQV�IRU�VXFK�D�VWUXFWXUH❙ LQ�����\RXOO�OHDUQ�DERXW�ILHOG�SURJUDPPDEOH�JDWH�DUUD\V��)3*$V��WKDWDUH�MXVW�VXFK�SURJUDPPDEOH�PXOWL�OHYHO�VWUXFWXUHV

❘ SURJUDPPDEOH�PXOWLSOH[HUV�IRU�ZLULQJ❘ ORRNXS�WDEOHV�IRU�ORJLF�IXQFWLRQV��SURJUDPPLQJ�ILOOV�LQ�WKH�WDEOH�❘ PXOWL�SXUSRVH�FHOOV��XWLOL]DWLRQ�LV�WKH�ELJ�LVVXH�

❚ 8VH�PXOWLSOH�OHYHOV�RI�3$/V�3/$V�520V❙ RXWSXW�LQWHUPHGLDWH�UHVXOW❙ PDNH�LW�DQ�LQSXW�WR�EH�XVHG�LQ�IXUWKHU�ORJLF

Page 31: Combinational logic implementation Implementations of two level logic

CSE 370 - Spring 1999 - Combinational Implementation - 61

&RPELQDWLRQDO�ORJLF�LPSOHPHQWDWLRQ�VXPPDU\

❚ 0XOWL�OHYHO�ORJLF❙ FRQYHUVLRQ�WR�1$1'�1$1'�DQG�125�125�QHWZRUNV❙ WUDQVLWLRQ�IURP�VLPSOH�JDWHV�WR�PRUH�FRPSOH[�JDWH�EXLOGLQJ�EORFNV❙ UHGXFHG�JDWH�FRXQW��IDQ�LQV��SRWHQWLDOO\�IDVWHU❙ PRUH�OHYHOV��KDUGHU�WR�GHVLJQ

❚ 7LPH�UHVSRQVH�LQ�FRPELQDWLRQDO�QHWZRUNV❙ JDWH�GHOD\V�DQG�WLPLQJ�ZDYHIRUPV❙ KD]DUGV�JOLWFKHV��ZKDW�WKH\�DUH�DQG�ZK\�WKH\�KDSSHQ�

❚ 5HJXODU�ORJLF❙ PXOWLSOH[HUV�GHFRGHUV❙ 520V❙ 3/$V�3$/V❙ DGYDQWDJHV�GLVDGYDQWDJHV�RI�HDFK