Half Adder


 

   !#"#$#%'&(&*),+!+!. /102436587:9=@??A BDC8EGFIHKJ6LNMPOQORTSUHVFWXEVYZC\[LZS]RT^XL _`CaOQObC\J]cbWXdeRTCafXcQYZgih jlk FOm_FNEXEXLZS jon@pXq RrSTFY(RTCaSes`_ p ObOFNWXE:^XFOQ_Tt jlu LZYZcQvwFNOFEXExcQRTcQCaWys{z| u FExEXLZSTt jl}~ Fv€fXOQL fXSrC q ObLZv€g ƒ‚'„Z…N†‡‚'ˆ#ˆŠ‰ ‹ ŒFgUReRrcbv€LŽJ6LEXcbgY p ggrLZEFV_ p ObO‘FNEXEXLZSi’VB^XLw^GFNOQ_FNEXEXLZScbg“[aLiSHygrcQvcQO”FS•L ~ YZLifxR Rr^GFNR]cmR]EXC@Lig]WXCR]^GFI[aLeFŽYIFSSH–cQW’B^XL q ObC8Y˜—wExc”FdaSrFvcQgZh ™ š a

f

Half Adder

b

cout

B^xLŽ^GFOQ_FEXEXLiS›WXLZLiEXg RTC–FNEXEŠRœJ6C–cQWXf p Rrg•RTCdaLiRr^XLZS FNWXE#fXSrC8E p YiLŽFKg p vFWxEžF YZFSrSUH q cmRI’B^XL RTS p RT^VR˜F q ObL cQgRT^XLiWh F q Ÿ¡ £¢¡¤ _ ¥ ¥ ¥ ¥ ¥ ¦ ¥ ¦ ¦ ¥ ¥ ¦ ¦ ¦ ¦ ¥ ¦

§¨C p gr^XC p ObEŠSLZYiCadaWXcQ©ZL Ÿ¡ £¢¡¤ Fg Ÿ( £¢¡¤ª«­¬ FWXE Rr^XL!g p v®C p RTf p RI¯4_°¯4Fg›± ª«“²³¬ ’ ´µL“YIFWVRT^xLZW¶EXSTFIJ·Rr^XL“^GFOm_”¸°FEXExLZSYicbSrY p cQRZh ¹ a

f

b

º»

cout

V¼ ½ „I„o‚'ˆ#ˆŠ‰ ‹†¾‹‰ ¿#‹‘ÀIÁ‰ œWRT^XL>O”FgURObLiYiR p SrL,J6L•RTFOb—NLZEwF q C p R^XC\J³RrC!cbv€fXObLivLiW1R6F“_ p ObOÃFExEXLZSi’‘Ä>C\JÅRT^GFNR JL–^GFI[aLKRr^XL–^GFOm_,FEXEXLiS p WXExLZSŽC p S q LiOQRTgeJ6L–YZFWFYiR p FOQOQH qXp cQObEÆF _ p ObOFEXEXLiS _`SCavÇFŠfGFcbS'C_,^GFOQ_,FNEXEXLZSgFWXECaWXLKFEXEXcmRTcbCWGFO6ȓÉÊd1FNRrL’yB^XL–YZcQSrY p cQR!OQC@C—8g OQcb—NLh a b

Ì

c in

Ë ÍÌ

Half c Adder s

Ë ÌÍ

Half Adder

Ì

c s

Í

c out sum

Full Adder

Î ½#Ï Ð ‹‚!Ñ ÐÒ ‹‘Á ´µLYIFW qXp ObE q CRT^V_ p ObOFNWXE:^XFOQ_g pXq RrSTFY(RTCaSgZ’ÓÔ_ p OQOg pXq RTSTFNYiRTCS>g pXq RTSrFYiRrg>RœJC W p v q LiSrgZ¯F–FNWXE q ¯ÕRrCadaLiRr^XLZS›J]cmRT^#F q CaSSrC\JcbWŠRTCwfXSrC8E p YiL!RT^XLŽEXcmÖÕLiSrLiWXYZLFWxE F q CaSSrC\JÊC p RTf p RI’µÓ×^GFOm_]g pXq RrSTFY(RTCaSŽg pXq RrSTFY(RTgŽRœJ6CžW p v q LZSgZ¯¨F#FWXE q ¯¨FWxE fxSrC8E p YZLig,Rr^XL“EXcQÖ4LZSLZWXYiLFWXE:F q CaSSrC\J·C p RTf p RI’‘B^XL q ObC8Y˜—wEXcbFdaSrFvg6ObC8Ca—OQcb—NLh Ø

a

Ù

b out

b

Ú

Full Subtractor

a

b in

b out

b

Û

Half Subtractor

d

d

›Ü Ý ÞÞßXÝ à>áxâGãäÕáXå¨â BDC p WXExLZSrgUR˜FWxEžJ]^XFNR•Rr^Xcbg›YicbSY p cmR•cQg•g p fXf4CgrLZE#RrC–EXCKObL(RIMæg>RTF—LFwYiObCagL!ObC8Ca—VFNR FNW¶L ~ FvfxObL C_ q cbWGFNSHKg pXq RrSTFY(RTcbCWh b out = 1

b out = 1

-

02 0010 1001 1001

b in = 0

B^xL q CaSrSCçJcbWÅRTCRT^XLžèGSrgURŠg pXq RTSrFYiRrcbCaWécbg¶©ZLiSrC q LiYIF p gLêWXCNRT^XcQWXdl^XFg q LZLiW q CaSSrC\J6LiE:HLiRI’6B^XLZW JLWXLZLiE RTC€g pXq RTSTFNYiR ¦ _`SCav ¥ ’¨´êL“YIFNWMæR>EXCRT^GFëR•CaW¶C p S C\J]WìgrCžJ6LVWXLiLZEìRTC q CSrSrC\JíCaWXL–_`SrCvÇRT^xL¶WxL ~ RwW p v q LiSF q C\[L p g°¸“RT^GFëRgLiRrg C p RRrC ¦ ’wÄ,C\JJLYZFWµg pXq RrSTFY(R¸>J6L q CSrSrC\JLZEž_`SrCav®RT^XLWXL ~ Re^XcQda^XLZS qExcbCadaScmSrRC\Jî grCŽRT^XFNR,dacQ[LZg p g,F!RTCRTFOC_ Ø RrCŽJ6CaS—wJ]cQRr^’,s Ø ¸ ¦ t ª ¦ gC€C p S]E¶cQg ¦ ’ B^xL!WXL R g RrSTFY(RTcbCWŠJFW1Rrg•RTCKg RrSTFY(R ¥ _`SrCav ¦ ’•É,LivLiv LZSZ¯ÃRT^XC da^¯ÃRT^GFNR JL^GFNEŽ~ F q CapXSrq SC\Jï_`SrCav q Li_`CaSL’B^XpXFNRq v€LIFWxg q CaSrSCçJcQW'cQg ¦ ’ n C•q èGSgRRTCKRT^xL'_ p ObOF q C p R ¬˜ £¢¡¤ ŒÿLiRIMæg,ObC8Ca—wFëR,F“FSWGF p d^:vFfh    ab

00

01

11

10

0

0

1

0

0

1

1

1

1

0

b in

¬˜ £¢¡¤ª «  ¬l«  ¬Tôöõ!쬡¬˜ôþõ ª « ¬ s « a²ò¬ t ¬˜ôþõ |6CvfGFNSrL›RT^XFNR]RTCŽJ]^GFNR]JL^XFE¶_`CS Ÿ( £¢¡¤ cbW–RT^xL“_ p ObOÿFExEXLZSih Ÿ( £¢¡¤ª·«­"¬  s «›²o¬ t Ÿ¡ôöõ nCN_CeYZHaC C p SrgrYILNF¯ÕWvdaFLi—R6LiFg›_ fÃp LZObOGS_`g LipxYiq R•RTgrSrLZFWxYigrRrLŽCaS¨grcQ_`WXSCaYZvLHaFC _ p YIObO‡FFWŠEXg ExLZS Rrq STFH€Y(YiR•CaRœvJfxC–ObLZW v€v LZW1RrLicbWXSrgdFxH:’BYZC^xvcbgZ¸ ¯ p p pXq p q q fxObLZv€LZW1RrcbWXdŽCaWxLCN_À%$ ‚!„&# À%'€À Ð)( ˆ#ˆ#À Ð À Ò+* ,.-0/ # 1 ÿŒ L(RIMæggTFIHwJL›J6FW1RRTC qXp cbObEwF!YZcQSrY p cQR¨RT^GFNR6J]cbObOÃFExEKRœJ6CEXLiYZcbvFOÃEXcbdcQRTg¨cbWKz| u _`CSrvRTCadaL(RT^XLiS•J]cQRr^žFKYIFSSH cbWXf p RI¯fXSC@E p YZcQWXdwRT^xLZcbS•g p vFWXEyFKYIFSSH:C p Rrf p RI’ k cQC\RTJgi¯ÕFNvwWXFEžW1HžFwYIcQWXFNf SrSp H¶Rrg'cQWEX’•C¶BJ6^XLKcQg•^XvF\[FL — LigB2x^X’ LiSrL–C\JFSL€F RœC JC#R›zC | RTu f W RTgp v ´êq LiLeSrgZ^G¯FILI[aFLŽY˜^êCaWxJ]LecmRT_`^C  S q k q p p p  p q cQR]C p Rrf p R,FWxE¶Rr^XL“YIFSSH–C p R,_`CS]FŽRrCR˜FNOC_3@’B^XL q ObC8Y˜—wEXcbFdaSrFvOQC@Ca—­gOQcb—NLh 3

5 5 5 5

4 4

y3 y2 y1 y0

x3 x2 x1 x0

6

Decimal Digit Adder c out

(DDA)

6

c in

´µL YZC p ObEVvF—L“F72 q cQR6R˜F q OQL FWXEVfXSC@YiLZLiE¶_`SCavíRr^XLZSL p grcbWxd!RT^XL“gTFNvL fXSC@YiLZgg JLMð[aL q LiLZW p grcQWXdX’´µL“YZC p OQE¶FObgC€ExC€Rr^XLFEXEXcmRTcbCWKcbW¶F q cbWXFSHK_`CSrv¶’ ´Å^XFNR F q C p R>C p S,C p Rrf p R  Âú_Rr^XL'g p v cbg,daSrLZFNRTLiS,Rr^GFW ¦\¥ J6L'WXLZLiEŠRTCwg pXq RrSTFY(R ¦I¥ _`SCavcmRFWXEžgrL(R“RT^XLYIFNSrSHŠC p R RTC ¦ ’z p R^XC\JîYIFNWyJLg pXq RrSTFY(R ¦\¥  ´µLZOQO£¯ JL'LicQRr^XLZS qXp cQObE:FYZcQSrY p cQR]RTCg pXq RTSTFNYiR ¦I¥ CaS,CaWXL“RTCwFEXE:¸ ¦\¥ ’z p R>J]^GFëR›cbg¸ ¦I¥  s 9¦ 8 ¸ ¦\¥ t ª 8 ’´êL“YZC p ObE–RT^xLZSrL(_`CaSrLFExE 8 cbWxgRTLZFE’ ´µLMæObOÕYZCaW1RTcQW p L RT^XLz| u FEXEXLiS,cQW–RT^XL“WXL ~ R,OQLZYiR p SrLN’Q’m’

8