进位选择加法器之设计
¶i¦ì¿ï¾Ü¥[ªk¾¹¤§³]-p 179
¶i¦ì¿ï¾Ü¥[ªk¾¹¤§³]-p
Á»àÀ²¡B¸³¬î·¾¡B§õ¤å¯q
¶Ô¯q§Þ³N¾Ç°|¹q¤l¤uµ{¨t
ºK-n
¶i¦ì¿ï¾Ü¥[ªk¾¹ (Carry Select Adder; CSA)³Ìªìªº³]-p¬O¬°¤F¥i¥H°õ¦æ°ª³t
¥[ªk¹Bºâ¡A¦ý¬O¨ä¥N»ù¬°Ò¨Ï¥Îªº¹q¸ô-±¿n¤Ó¤j¡AÒ¥H¡A¦b¤§«áªºCSA ³]-p¤j¦h¬O°Q½×¦p¦ó´î¤ÖC SA ¹q¸ôªº-±¿n¬°¥D¡CCSA ¥i¥ÑÂùº§ªi ¶i ¦ì¥[ªk ¾¹ (Ripple Carry Adder; RCA)ªº¹q¸ôµ²ºcÒ²Õ¦¨¡A²M µØ¤j ¾±Çi ¼y ¤¸±Ð±Â[2]´£¥X¥H¤@-Óº§ªi ¶i ¦ì¥[ªk ¾¹»P¤@-Ó¡u¥[1(Add One)¹q¸ô¡vªº¹q¸ôµ²ºc¨ú¥N¡C¦b¥»¤å¤¤¡A´£¥X¤@ºØ·sªº¥[1¹q¸ô¤Î¦h¤u¾¹ªºµ²ºc¡A¨Ï±oCSA ¦b¹q¸ô-±¿n¤W¥i¥H¤j´T´î¤Ö¡F¥H64¦ì¤¸¥[ªk¾¹¦Ó¨¥¡A¨Ï¥ÎUMC 0.5um¤§»sµ{§Þ³N¡A¸g¥Ñ¹êÅçµ²ªG±oª¾¡G ¥»¤å´£¥X¤§§ï¨}¦¡¶i ¦ì¿ï¾Ü¥[ªk ¾¹µ²ºc¸û¤§«eªº¶i ¦ì¿ï¾Ü¥[ªk ¾¹µ²ºc¸û¤§«eªº¶i ¦ì¿ï¾Ü¥[ªk ¾¹¦b¹q´¹Åé-ӼƤW¤Ö¤F±Nªñ13.74%¦Ü27.17%¡A¦Óµ¿ðɶ¡«h¦³2.34%¦Ü22.33%Àò¯q¡C
ÃöÁäµü¡G¶i ¦ì¿ï¾Ü¥[ªk ¾¹¡B-pºâ¾÷ºâ³N¡B¥[ªk¾¹³]-p¡Bºâ³N¹q¸ô³]-p
1. ¬ã¨s-I´º
¥[ªk¹Bºâ¬°-pºâ¾÷¤¤³Ì°ò¥»¤]¬O³Ì-«-nªº¹Bºâ¡A¦]¨ä¤j¶qÀ³¥Îó¼Æ¦ì«H¸¹
³B²z¾¹¡BÂoªi¾¹¡B¿n¤À¾¹¡B-¼ªk¾¹¡B°£ªk¾¹¡B°ª³t¹Bºâ¹q¸ôµ¥ªº³]-p¡A¬G¥[ªk¾¹(Adder)¹ê¬°¤@¤Á»Ý-n¤j¶q-pºâªº³B²z¾¹¤§ºc¦¨°ò¥Û¡A¬G-Y¯à´£¤É¥[ªk¾¹ªºÄ¯à·N§Y¥i¤j´Tªº§ïµ½-pºâ¾÷ιBºâ³B²z¾¹¿nÅé¹q¸ôªºÄ¯à¡C¥[ªk¾¹¹q¸ô³]-p¤è¦¡¥i°Ï¤À¬°¨â¤jÃþ:²Ä¤@Ãþ¨ã¦³µ²ºc³W«h¤Î¹q¸ô²³æ¤§¯SÊ¡A¦ý¬O¹Bºâ½ÆÂø«×«o»P¥[ªk¹Bºâ¤¸¤§¦ì¤¸¼Æn ¦¨¥¿¤ñ¡Aº§ªi ¶i ¦ì¥[ªk ¾¹¡]Ripple Carry Adder¡F R C A¡^
§Y Äݦ¹Ã;¥þt ¤@Ãþ«h µÛ-«§ïµ½¹B ºâ³¡A¨t «×ϱo ¹B ºâ½ÆÂø«×-°§C ¬°¥[ªk ¹B ºâ¤¸¤§¦ì¤¸¼Æªº¹ï¼Æ-¡A¦Èý¬O ¹q ¸ô¸û½ÆÂø¦Ó¥B µ²ºc ¤£³¡A¦W «]h ¦Ó»Ý-n ÃB ¥~¤§´¹¤ù-±¿n ¹ê²{¦¹Ãþ¥[ªk ¾¹¹q ¸ô¥H «e ¤¦¡¶i ¦ì¥[ªk ¡]¾¹Carry Lookahead Adder¡FCLA¡^¡B¶i¦ì¿ï¾Ü¥[ªk ¾¹¡]Carry Select Adder¡FCSA¡^¡B¶i ¦ì¸õÅD ¥[ªk ¾¡]¹Carry Skip Adder¡FCSK¡^µ¥¬°¥N ª¡íC¦ý¦¹¤GªÌ¹q ¸ô¯S ¬ÊÒ»P¥þ¥[¾¹³]-p ¤§Àu ¦H ¦³¡A¨Ã¬Ò¼sªx¨Ï¥Î󤣦PÃöÀ³¥Î¥Øªº¤§°ª³t ¹B ºâ¹q ¸ô³]-p ¡C ¤¤
¥[ªk¾¹ªº³t«×»P-±¿n¹ïÒ³]-pªº¹q¸ô¦³µÛÁ|¨¬»´-«ªº¼vÅT¡CRCA´£¨Ñ¤F¤@-Ó³W«hʪº³]-p¡A¥B¨ä¦b-±¿nªº¨Ï¥Î¤è-±¤]«Ü¤Ö¡A¦ý¬O¨ä¥»¨-ªºµ¿ðɶ¡«Üªø¡A¦ÓCLA ¥D-n¬O¬°¤F§ïµ½RCA ¦bµ¿ðɶ¡¤Wªº¯ÊÂI¡AÒ´£¥Xªº¤@ºØ³]-p¡A¦ý¨ä¨Ï¥Îªº´¹¤ù-±¿n¤Ó¤j¡AÒ¥H«á¨Ó´£¥XªºC SA ¤ÎCSK ³£¬O¬°¤F¦b-±¿n»P³t«×¤§¶¡¨ú±o¤@-Ó¥-¿Å¡A¦Ó¨âªÌ¦b¹q¸ôªº-±¿n»P³t«×¤W¤]¦³µÛ¤£¤@¼Ëªº¯SÊ¡ACSA ªº³t«×¸ûCSK §Ö¡A¦ýҨϥΪº-±¿n¸ûCSK
180 ¶Ô¯q¾Ç³ø²Ä¤G¤Q¤@¨÷²Ä¤G´Á
¤j¡C¦pªí1ҥܡARCA ¥»¨-´£¨Ñ¤@-Ó²¼äªº³]-p¡A¦]¨ä´¹¤ù-±¿n½ÆÂø«×¬°O(n)¡A¦ý¨ä-pºâ½ÆÂø«×¬°O(n)¡A»Ý-nªá¶OªºÉ¶¡¸ûªø¡C¦ÓCLA -pºâ½ÆÂø«×¬°O(log n )¡AÁöµM³t«×§Ö¡A¦ý¨äªá¶O-±¿n«Ü¤j¡A¨ä´¹¤ù-±¿n½ÆÂø«×¬°O(n log n)¡C¥ÑóRCA »PCLA ¦b¹ïó-±¿n¤Î³t«×¤W¤£¯à-ÝÅU¡AÒ¥H«á¨Ó¤~·|¦³CSA ¤ÎCSK ªº²£¥Í¡CCSA»PCSK ¦¹¨âºØ¥[ªk¾¹¬O§é°JóRCA»PCLA ¤§¶¡ªº¥[ªk¾¹¡A´N-±¿n¦Ó¨¥¡ACSK ¸ûCSA ¤Ö¤F±Nªñ35¢M¡A¦ÓCSA ¦bɶ¡¤W¤ñCSK §Ö¤F30¢M¡C¦pªG¡A¦b¤@-Ó¤¤µ¥°õ¦æ³t«×ªº¥[ªk¾¹¡A¨Ï¥ÎCSK ·|¤ñ¨Ï¥ÎCSA ¬°¨Î¡A¦]¬°¦b¤£-n¨D³t«×ªº±¡ªp¤U¡A·íµM¿ï¾Ü-±¿n¤W¸û¦ûÀu¶ÕªºCSK¡C
ªí1 ¥[ªk¾¹¤§¤ñ¸û[9]
µù¡G¦b¤@-Ó¤¤µ¥°õ¦æ³t«×ªº¥[ªk¾¹¡A³q±`¨Ï¥ÎCSK
¦p¹Ï1 ҥܡACSA ªº°ò¥»·§À¡A¤D¬O±N¨â²Õº§ªi ¶i ¦ì¥[ªk ¾¹¤À§O¥H¶i¦ì¿é¤J
(Carry-In; Cin)«H¸¹ Cin=0¤ÎCin=1°µ¬°°²³]¡A¥h¥-¦æ°õ¦æ¨â²Õ¥[ªk¹Bºâ¡A²£¥Í¦U¦Ûªº¿é¥X¡A¦A¥H¥¿½TªºC in «H¸¹±±¨î¦h¤u¾¹¿ï¾Ü¥X¥¿½Tªºµ²ªG¡F¦p¦¹¡A¥i¥H¤£¥Î¹³RCA¤@¼Ëµ¥«Ý«e¯Å¶i¦ì¡A¦Ó¥ý¦æ¹Bºâµ²ªG¡A «K¯à¬Ù¤U-ì¨Óµ¥«Ý«e¯Å¶i¦ìªºÉ¶¡¡C¦Ó¦bCSA ¤¤³Ì-«-nªº¤¸¥ó¬°¦h¤u¾¹¡A¦pªG¨S¦³¦h¤u¾¹¡A«KµLªk°õ¦æ¿ï¾Üªº°Ê§@¡C °ò¥»¤W¡A¥u-n¯à§¹¦¨¥[ªk¹Bºâ¥\¯àªº¹q¸ô¡A«K¥i¨Ï¥Î¦bCSAªº¥[ªk°Ï¶ô¤¤¡C¥Ø«eCSA ªº¥[ªk°Ï¶ô³£¬O¨Ï¥ÎRCA»PCLA ªº¹q¸ô¼Ò²Õ¡C
Cout si+m-1si
¹Ï1¡G °ò¥»¶i ¦ì¿ï¾Ü¥[ªk¾¹µ²ºc¹Ï
¶i¦ì¿ï¾Ü¥[ªk¾¹¤§³]-p 181 2. ¶i¦ì¿ï¾Ü¥[ªk¾¹¤§³]-p2.1 ¶Ç²Î¶i¦ì¿ï¾Ü¥[ªk¾¹
¶Ç²ÎC SA ¬O¨Ï¥Î¨â-Ó¬Û¦Pªº¥[ªk°Ï¶ô¡A¤À§O°²³]Cin=0¤ÎCin=1¥h¶i¦æ¥[ªk
¹Bºâ¡A¦p¹Ï2¡]a¡^¬O¤@-ÓC SA ¨Ï¥ÎÂùRCA ¼Ò²Õªº¹q¸ô¡A¨ä¨C¤@-Ó¥[ªk°Ï¶ô³£¥i¥H¥ý¦æ°²³]Cin ¥h¶i¦æ¹Bºâ¡AµM«á¤À§O±N¹Bºâµ²ªG°e¦Ü¦h¤u¾¹¡Aµ¥«Ý¥¿½TªºCin ¨Ó¿ï¾Ü¥X¥¿½Tªºµ²ªG¿é¥X¡A³o¼ËÁöµM¥i¥HÁYµuº§ªi¶i¦ìªºªøµ¥«Ýɶ¡¡A¦ý¬O¡A¦p¦¹ªº§@ªk¨ä-±¿n·|¼W¥[¦Ü-ì¨Óªº¨â-¿¡AÒ¥H³oºØ§@ªk¤£ºâ¬O³Ì¦nªº¡A¤U-±´N¬O-n¤¶²Ð¥t¥~ªº¹q¸ôµ²ºc¡A·|¨Ï±o¨ä¹q¸ô-±¿n´î¤Ö¦Ü-쥻ªº75¢M¡C
¡]a¡^¶Ç²Î¶i ¦ì¿ï¾Ü¥[ªk ¾¹
¡]b¡^¨Ï¥Î¥[1¹q¸ô¤§¶i ¦ì¿ï¾Ü¥[ªk ¾¹
¹Ï2¡G¶i ¦ì¿ï¾Ü¥[ªk¾¹µ²ºc¹Ï[10]
2.2¨Ï¥Î¥[1¹q¸ô¤§¶i¦ì¿ï¾Ü¥[ªk¾¹
¦¹¤èªk¤D¬O¥H¤@-ÓRCA »P¥[1¹q¸ô¡A¥h¨ú¥N-쥻ÂùRCAªº¹q¸ô¡A¦p¹Ï2¡]b¡A ¡^
§Ú-Ì¥H¤@-ÓR CA ¥h¹BºâCin=0ªºµ²ªG¡A¦A¥H¥[1¹q¸ô±N¦¹µ²ªG¥[1¡A²£¥Í¥HCin=1ªº¹Bºâµ²ªG¡A¦p¦¹«K¥i§¹¦¨¤À§O¥HCin=0¤ÎCin=1ªº-pºâ¡A¹F¨ìCSAªº°Ê§@-n¨D¡C³o¬O¤@ºØ·sªº§@ªk¥i¥H¤£³z¹L¥[ªk¹Bºâ±o¨ìCin=1ªºµ²ªG¡A¥Ñ¹Ï3¨Ò¤l¥iª¾¡A¥[1¹q¸ô¬O¬°¤F¨ÏCin=0ªº¹Bºâµ²ªG¥[1¡A¦Ó±o¨ìCin=1ªºµ²ªG¡A¦ý¬O¡A§Ú-̵o²{¦pªG¥Ñ³Ì«á¤@-Ӧ줸¶}l¹«e´M§ä²Ä¤@-Óªº¹s(ºÙ¬°First Zero)¡A¦A±NFirst Zero¤Î¨ä¸û§Cªº¦ì¤¸¤Ï¬Û¡A ¨äµ²ªG»PCin=0¸g¹L¥[ªk¹Bºâ¥[1ªºµ²ªG¬Û¦P¡A ¦p¦¹«K¤£¥Î³z¹L¥[ªk¹Bºâ±o¨ìC
in=1ªºµ²ªG¡CFirst Zero¨Mw¨C-Ӧ줸¬O§_»Ý-n³Q¤Ï¬Û¡AFirst Zero§ä´M¹q¸ô¥i¥Ñ¹Ï7¤¤¶¡ªºNMOS¤ÎPMOS Ãìºc¦¨¡C
¹Ï3¡G First Zero¨Mw¨C-Ӧ줸¬O§_»Ý-n³Q¤Ï¬ÛªºÁ|¨Ò[10]
182 ¶Ô¯q¾Ç³ø²Ä¤G¤Q¤@¨÷²Ä¤G´Á
¥[1¹q¸ô(Add-One Circuit)¦p¹Ï4¤¤¶¡Ò¼Ð¥Ü¥X¨Óªº³¡¥÷¡A¥þ¥[¾¹²£¥ÍÒ¦³ªºM¤Î¸É¼ÆªºM¡A¸g¥ÑNMOS¤ÎPMOS Ãìºc¦¨ªºFirst Zero§ä´M¹q¸ô¨Mw¥XCin=1ªºµ²ªG¡A¦A¥ÑCin ±±¨î¦h¤u¾¹¿ï¾Ü¥XSk (¨ä¤¤k=0,1,2,3)θɼÆSk¡A¦pªG¡A±±¨î°T¸¹¬°¹s¡A¦h¤u¾¹¿ï¾ÜSk¡A§_«h¡A¦h¤u¾¹¿ï¾Ü¸É¼ÆSk¡C
¹Ï4¡G ¨Ï¥Î¥[1¹q¸ô¤§¶i ¦ì¿ï¾¥Ü[ªk ¾[2¹]
¦p¹Ï4ҥܡA¦bCSA ¹q¸ô¤¤³Ì-«-nªºÀ³¸Ó¬O¦h¤u¾¹¡A ¦pªG¨S¦³¦h¤u¾¹«KµLªk
¹F¨ì”¿ï¾Ü”ªº°Ê§@¡C¦Ó¦h¤u¾¹²Õ¦¨ªº¤è¦¡¦³«Ü¦h¡A ¦Ó¦b²M µØ¤j ¾±Çi ¼y ¤¸±Ð±Â´£¥X¤§¡u¨Ï¥Î¥H¤@-Óº§ªi ¶i ¦ì¥[ªk ¾¹(RCA)»P¥[1(Add One)¹q¸ô¡v³]-p ªº¶i ¦ì¿ï¾Ü¦¡¥[ªk ¾¹[2]ҨϥΫK¬O¥HNAND ¹q¹h²Õ¦¨ªº¦h¤u¾¹¡A¦p¹Ï5¤¤i¥Ü¡A¨ä¹q¸ôµ²ºc¤Î¯u-Ȫí¡A¦¹ºØ¦h¤u¾¹»Ý-n¨Ï¥Î¨ì3-ÓNAND ¹q¹h¤Î1-ÓNOT ¹q¹h¡A¦Ó±N¦¹¦h¤u¾¹M¥Î¦b¹Ï4¹q¸ô¤¤¡A±N·|¨Ï¥Î¨ì¸û¦hªº¹q¹h¡A¥[¤W¨äÒ¦³ªº¼Ò²Õ¬Ò¬O±Ä¥Î¥þ¤¬¸É¦¡CMOS ¹q¸ô³]-p§Þ¥¡AÒ¥H¾É-P¹q´¹Åé¼Æ¶q«Ü¦h¡AÒ¥H¦b-±¿nªº¦Ò¶q¤W¨Ã¤£ºâ¬O³Ì²z·Q¡C
S1
Cout
1A 2
12
A
Y B
3
12A
Y B
3
Cin
12
A
Y B
S0
3
¹Ï5¡G ¥ÑNAND ¹q¹h²Õ¦¨¤§¦h¤u¾¹
2.3 §ï¨}¦¡¨Ï¥Î¥[1¹q¸ô¤§¶i¦ì¿ï¾Ü¥[ªk¾¹
¦b¹Ï4¹q¸ô¤¤¡AҨϥΨ쪺¦h¤u¾¹µ²ºc¡A¬°Âù¼h¦h¤u¾¹(Two Level Multiplexer¡F
TMUX) ¡AÒ¥H¨C-Ӧ줸³£»Ý-n¥Î¨ì¨â-¿ªº¦h¤u¾¹-±¿n¡A¦]¦¹´£¥X¤@ºØ¥H1-Ó¦h¤u¾¹¤Î1ªºNAND ¹q¹h¨Ó§¹¦¨³oºØTMUX¤§µ²ºc¡A¦p¹Ï6ҥܡA¨ä¦¡¤l±À¾É¦p¤U¡G
¶i¦ì¿ï¾Ü¥[ªk¾¹¤§³]-p 183
S =A ⋅Sel 1+B ⋅Sel 1⋅Sel 2+A ⋅Sel 2
()
=A ⋅Sel 1⋅Sel 2+B ⋅Sel 1⋅Sel 2+A ⋅Sel 2
=A Sel 1⋅Sel 2+Sel 2+B ⋅Sel 1⋅Sel 2 =A Sel 1+Sel 2+B ⋅Sel 1⋅Sel 2
((
)
=A (Sel 1⋅Sel 2) +B Sel 1⋅Sel 2 ) -------------------------------------- (1)
S e l1
=
Sel1 Sel2
S A B A A
0 0 1
0 1 0 1
S e l2
¹Ï6¡G Âù¼h¦h¤u¾¹µ²ºc¤Î¯u-Ȫí
1
¦p¦¹¡A§Y¥i±N-쥻TMUX µ¥Ä¦¨1-Ó¦h¤u¾¹¤Î1-ÓNAND ¹q¹h¡A¹Ï6«K¬O³o¨âºØÂù¼h¦h¤u¾¹ªºµ²ºc¤Î¯u-Ȫí¡A¥Ñ¯u-Ȫí¥iª¾¦¹¨âºØ¦h¤u¾¹ªº¥\¯à¬Û¦P¡A¦ý²Ä¤GºØTMUX ¨ä¥»¨-ªº¦h¤u¾¹¡A¤D¬O±Ä¥Î¥Ñ¶Ç¿é¹h(Transmission Gate¡FTG)²Õ¦¨¤§¦h¤u¾¹¡ATG ¦h¤u¾¹¬O¤@ºØ§Ú-ÌÒ¼ô±xªº¦h¤u¾¹¡A¦p¹Ï7ҥܬ°¨äµ²ºc¤Î¯u-Ȫí¡AÒ¥H·|¸û¹Ï5ªº¦h¤u¾¹¤Ö±¼¤F³\¦h¹q´¹Åé¡A ·|¤ñ-쥻ªº¹q¸ôµ²ºc§ó¸`¬Ù-±¿n¡C±N¦¹TMUX ¹q¸ôÀ³¥Î¦b¨Ï¥Î¥[1¹q¸ô¤§¶i ¦ì¿ï
¾Ü¥[ªk ¾¹¤¤¡A¦¹«K¬°§ï¨}¦¡¨Ï¥Î¥[1¹q¸ô¤§¶i¦ì¿ï¾Ü¥[ªk ¾¹¡A¦p¹Ï8Ò¥Ü[10]¡A ¨ä¹q¸ô-×¥¿¦p¹Ï9ҥܡA¦p¦¹¡A´N¯à«O«ùKim’s CSA¹q¸ô¥¿½T°Ê§@¡C
sel 0
1
s X Y
¹Ï7 ¥Ñ¶Ç¿é¹h²Õ¦¨¤§¦h¤u¾¹¤Î¯u-Ȫí
184 ¶Ô¯q¾Ç³ø²Ä¤G¤Q¤@¨÷²Ä¤G´Á
¹Ï8 -ìlKim’s CSA [10]
¹Ï9 -×¥¿Kim’s CSA
2.4 ´£¥X¤§§ï¨}¦¡¶i¦ì¿ï¾Ü¥[ªk¾¹
§Ú-Ì´£¥X¤§§ï¨}¦¡¶i ¦ì¿ï¾¥Ü[ªk ¾¹q¸ô¹¡A ¥D-n±N«e-z¨âºØ¶i ¦ì¿ï¾¥Ü[ªk ¾¹¹q¸ô°µ¤@-Ó¾ã¦X¡A¥Øªº¬O´î¤Ö¶i ¦ì¿ï¾¥Ü[ªk ¾¹q¸ô-±¿n¹¡A¨Ï¨ä¹q´¹Åé-Ӽƴî¤Ö¡A¨ä¹q¸ô¦p¹Ï10ҥܡC¦ÓTMUX ¤è-±¡A±Ä¥Î³q¶Ç¹q´¹ÅéÅÞ¿è(Pass Transistor Logic¡F
PTL)³]-p¤è¦¡¡A±N¹q¸ôµ²ºc¥[¥H§ï¨}¡A¦p¦¹¡A-쥻¦bKim’s CSA»Ý-n12-Ó¹q´¹Åé¡A²{¦b¥u»Ý-n6-Ó¹q´¹Åé´N¥i¥H§¹¦¨¡A ¦p¹Ï11¹q¸ôҥܡA¦Ó¨Ï¥Î¦¹¹q¸ô·|¨Ï¨ä¹q´¹Åé-ӼƤj´T´î¤Ö¡A¦bÁ`Å骺įà¤è-±¤]·|´£ª@³\¦h¡C
¶i¦ì¿ï¾Ü¥[ªk¾¹¤§³]-p 185
¹Ï10 ´£¥X¤§§ï¨}¦¡¶i ¦ì¿ï¾Ü¥[ªk ¾¹
¹Ï11 ´£¥X¤§§ï¨}¦¡TMUX
3¡B¹êÅçµ²ªG»P°Q½×
¥Ñ󥻬ã¨sª`-«ªº¬OCSA ªº§ï¨}»P³]-p¡AÒ¥Hª½±µ§ï¨}¨Ï¥Î¨ä¥L¬ã¨s½×¤å[1][3-8]
ªº¹q¸ô¡A¨ÃM¥Î¦ÜC SA ¹q¸ô¡A¥H«K´ú¶q¨äįà¡F°òóUMC 0.5um2p2m»sµ{§Þ³N¡A¥»¤åªºµ¿ðɶ¡¶q´ú¬Ò¬O¥HWorst-Case (¥ç§YÒ¦³ªºAn=1¡BBn=0¤ÎCin=1¡A¨Ï¨ä¨C¤@¶¥³£¦³¶i¦ì¤§±¡§Î²£¥Í)ªº±¡ªp¥h°õ¦æ´ú¸Õ¡A¨ä¿é¥X¤Jªi«¬¦p¹Ï12Ò¥Ü
¸g¥Ñ§Ú-Ì°w¹ï64¦ì¤¸¶i ¦ì¿ï¾Ü¥[ªk¾¹ªº´ú¸Õµ²ªG±oª¾¡A¨Ï¥Î¥[1¹q¸ô¤§¶i ¦ì¿ï¾Ü¥[ªk ¾¹ (Chang’s CSA)[2]¤£½×¦b¹q´¹Åé-Ó¼Æε¿ðɶ¡¤Wªº¦Ò¶q¡A³£¤£¬O«Ü²z·Q¡A¦Ó§ï¨}¦¡¥[1¹q¸ô¤§¶i ¦ì¿ï¾Ü¥[ªk ¾¹ (Kim’s CSA) [10]ªº¹q¸ôµ²ºc§ïÅÜ¡A Ò¥Hµ¿ðɶ¡¸ûChang’s CSAªºµ¿ðɶ¡µu¡A¦ý¨ä¹q´¹Åé-Ӽƨå¼´î¤Ö«Ü¦h¡A §Ú-Ì´£¥X¤§§ï¨}¦¡¶i ¦ì¿ï¾Ü¥[ªk ¾¹(Ours Proposed CSA)«h¦PɦҶq¨ì¹q´¹Åé-ӼƤε¿ðɶ¡³o¨â-Ó¦]¯À¡AÒ¥H¦b
186 ¶Ô¯q¾Ç³ø²Ä¤G¤Q¤@¨÷²Ä¤G´Á
¦¹¤TºØ¶i ¦ì¿ï¾Ü¥[ªk ¾¹ªº¤ñ¸û¤W¡A§e²{¤ñ¸ûÀu¨}ªºµ²ªG¡A¦b¹q´¹Åé-ӼƤW´î¤Ö13.74%¦Ü27.17%¡A¦Óµ¿ðɶ¡«h¦³2.34%¦Ü22.33%Àò¯q¡A¦p¹Ï13ҥܡC§Ú-Ì´£¥X¤§§ï¨}¦¡¶i ¦ì¿ï¾Ü¥[ªk ¾¹§G§½¹Ï«h¦p¹Ï14ҥܡC
¡]a¡^Sum³¡¥÷
¡]b¡^Carry³¡¥÷
¹Ï12¡G CSA(4-bit)¼ÒÀÀªi§Î
¡]a¡^Tr.-ӼƤñ¸û¹Ï
¡]
b¡^Delay Time¤ñ¸û¹Ï
¹Ï13 ¡G¤TºØ¶i ¦ì¿ï¾Ü¥[ªk¾¹ªº¤ñ¸û
¹Ï14¡G§Ú-Ì´£¥X¤§§ï¨}¦¡¶i ¦ì¿ï¾Ü¥[ªk ¾¹§G§½¹Ï
¶i¦ì¿ï¾Ü¥[ªk¾¹¤§³]-p 187 4. µ²½×
CSA ¥i¥ÑRCA(Ripple Carry Adder)»P¤@-Ó¡u¥[1¹q¸ô¡vªº¹q¸ôµ²ºc¨ú¥NÂùRCA ªº¹q¸ôµ²ºc¡A ¦Ó¥»¬ã¨s¤¤Ò´£¥X·sªº¥[1¹q¸ô¤ÎTwo-Level Multiplexer (TMUX)ªºµ²ºc¡A¨Ï±o§Ú-Ì´£¥X¤§§ï¨}¦¡¶i ¦ì¿ï¾Ü¥[ªk ¾¹¹q¸ô¦b¹q´¹Åé-ӼƤÎįà¤W³£¯à´£ª@¡A¥H64¦ì¤¸¥[ªk¾¹¦Ó¨¥¡A¥»¬ã¨sÒ´£¥Xªº§ï¨}¦¡¶i ¦ì¿ï¾Ü¥[ªk ¾¹¦b¹q´¹Åé-ӼƤW¤Ö¤F±Nªñ13.74%¦Ü27.17%¡A¦Óµ¿ðɶ¡«h¦³2.34%¦Ü22.33%Àò¯q¡C
°Ñ¦Ò¤åÄm
[1] E. Abu-Shama and M. Bayoumi, “A new cell for low power adders”, IEEE International
Symposium on Circuits and Systems ( ISCAS '96),, Vol. IV, pp.49 -52, 1996.
[2] T.-Y. Chang and M.-J. Hsiao, “Carry-select adder using single ripple-carry adder”,
Electronics Letters, Vol.34, Issue:22, pp. 2101 –2103,1998.
[3] M. B. Ghaznavi-Ghoushchi and A. R. Nabavi, “Isomorphic structured synthesis of half adder
and full adder”, Canadian Conference on Electrical and Computer Engineering (IEEE CCECE 2002), Vol.2 , pp.634 -639 , 2002.
[4] H.Lee and G . E Sobelman, “A new low-voltage full adder circuit”, Proceedings. Seventh Great
Lakes Symposium on VLSI, pp.88 –92, 1997.
[5] N. Weste and K. Eshraghian, “Principles of CMOS VLSI design, a system perspective”,
Reading, MA: Addison-Wesley, 1993.
[6] A.M. Shams and M.A. Bayoumi, “A novel low-power building block CMOS cell for adders”,
Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (ISCAS '98), Vol.2 , pp.153 -156, 1998.
[7] A.M. Shams and M.A. Bayoumi, “A new full adder cell for low-power applications”,
Proceedings of the 8th Great Lakes Symposium on VLSI, pp.45 –49, 1998.
[8] D. Soudris, V. Pavlidis, A. Thanailakis, “Designing low-power energy recovery adders based
on pass transistor logic”, The 8th IEEE International Conference on Electronics, Circuits and Systems (ICECS 2001), Vol.2 , pp.777 -780, 2001.
[9] A. Tyagi, “A reduced area scheme for carry-select adders”, Proceedings 1990 IEEE
International Conference on Computer Design: VLSI in Computers and Processors, (ICCD '90), pp.255 -258, 1990.
[10] Youngjoon Kim and Lee-Sup Kim, “A low power carry select adder with reduced area”, The
2001 IEEE International Symposium on Circuits and Systems (ISCAS 2001) , Vol.4 , pp.218 -221, 2001.
188 ¶Ô¯q¾Ç³ø²Ä¤G¤Q¤@¨÷²Ä¤G´Á