CSC 110 - Intro. to Computing Lecture 7: Circuits & Boolean Properties.
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l h0 , l 0l h0 &, l0 i h0 o h0 f= o s.kh l h0 , l 0l h0 &, l0 i h0 o h0 f= o s.kh l h0 , l 0l h0 &, l0 i h0 o h0 f= o s.kh l h0 , l 0l h0 &, l0 i h0 o h0 f= o s.kh
Hkkj r lj d kj ds bysDV ªkfu d ,oa l wpu k iz ks| kSfxd h foHkkx u s t u l q fo/kk d sUnz ksa d h ;kst u k d ks t u in d s iz R;sd xz ke iapk;r ksa@xz keksaf=os.kh d sUn z ksa d ks [ kksyu s g s r q ;g ;kst u k “kq: d h gSA bl ;kst u k ds vUr xZ r Hkkj r lj d kj l h/ks lHkh xz ke iapk;r ksa@xz keksa ,oa “ kgj h { ks=ksa d s okM ksZ a rd “kkld h; ,oa vU; l q fo/kkvksa d ks ,d gh dsUn z ij miyC/k d j ku k pkgr h gSA bl ;kst u k ds vUr xZ r iz,d f=os. khf=os. khf=os. khf=os. kh l q fo/kk d sUn zl q fo/kk d sUn zl q fo/kk d sUn zl q fo/kk d sUn z [ kksyk t k;sxkj kf”k fn ;s ;g d sUn z [ kksy ldrs gS aA l h0 ,l0 l h0 &,l0 ih0 oh0iz ks| kSfxd h foHkkx ds vUr xZr d k;Z dj j gk gS og j k’V ªh; l wpu k foK ku dsUn z ¼,u 0 vkbZ0l h0 ½ d h ft yk bd kbZ ;ksa l s lg;ksx ysd j bu dsUn z ksa d s [ kksyu s e sa lg ;ksx d j sxkA
t u in esa l h0 ,l0 l h0 &,l0 ih0 oh0 f=os.kh d sUnz [ kksyu s gsr q j k’V ªh; lwpuk foK ku dsUnz ¼,u 0 vkbZ0l h0 ½ d ysDV sªV fLFkr d k;kZ y; esa vkosn u fd ;k t k ldr k gSA ;kst u k ds ckj s esa vf/kd
t kud kj h www.csc.gov.in ls iz kIr d h t k ldr h gS ,oa
t u in d h cscl kbV www.allahabad.nic.in
l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z
1 - vkon sd lEcfU/kr xz ke iapk;r ;k okM Z d k fu okl h gksu k pkfg;sA2 - vkosn d d e ls d e 1 0 oha ikl ,oa ml s d EI;wV j d k K ku gksu k pkfg;sA3 - efgyk vkosn d d ks iz Fke oj h;r k n h t k;sxhA4 - vu q lwfpr t kfr @tut kfr d s vkosn d ksa d ks oj h;r k nh t k;sxhA5 - vxj iwoZ esa ml xz ke iapk;r esa d ksbZ l h0 ,l0l h0 d sUnz d k;Z d j j gk gS r ks n wl j k dsUn z [ kksyu s
d h vu q efr u gha n h t k;sxhA6 - vkosn d ds ikl iSu ] vk/kkj@bZ fid d ksM Z gksu k pkfg;sA
l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z [ kksyu s gsr q vko”;d mid j .k &l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z [ kksyu s gsr q vko”;d mid j .k &l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z [ kksyu s gsr q vko”;d mid j .k &l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z [ kksyu s gsr q vko”;d mid j .k &
d sUnz [ kksyu s gsr q d e l s ;w0 ih0 ,l0 @bUoVZ j gksu k vko”;d gSA
l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z ksa d s vUr xZr n h t ku s o kyh l q fo/k k;sa&l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z ksa d s vUr xZr n h t ku s o kyh l q fo/k k;sa&l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z ksa d s vUr xZr n h t ku s o kyh l q fo/k k;sa&l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z ksa d s vUr xZr n h t ku s o kyh l q fo/k k;sa&
bu d sUnz ksa ds } kj k eq [;r % Ld he] vk/kkj d kM Z cu k;k t ku k] eksckby o M hV h,p fj pkt Z d s l kFk N k=ksa d h vku ykbu i<+kbZ ] V ªsu o cl esa l hV d k vkj { k.kpj .k esa j kT ; l jd kj } kj k n h t kus okyh l q fo/kk,a Hkh bu dsUn z ksa ij miyC/k d jk;h t k;saxhA
u ksV % & u ksV % & u ksV % & u ksV % & ;kst u k ds ckj s e sa t ku d kj h r gl hy ,oa O ykd f LFkr L oku dsUn z ksa l s iz kIr d h t k ld r h gSA;kst u k ds ckj s e sa t ku d kj h r gl hy ,oa O ykd f LFkr L oku dsUn z ksa l s iz kIr d h t k ld r h gSA;kst u k ds ckj s e sa t ku d kj h r gl hy ,oa O ykd f LFkr L oku dsUn z ksa l s iz kIr d h t k ld r h gSA;kst u k ds ckj s e sa t ku d kj h r gl hy ,oa O ykd f LFkr L oku dsUn z ksa l s iz kIr d h t k ld r h gSA
l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh fu Eu cSu j d k mi;k sx Hkh d j ldsx hAl h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh fu Eu cSu j d k mi;k sx Hkh d j ldsx hAl h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh fu Eu cSu j d k mi;k sx Hkh d j ldsx hAl h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh fu Eu cSu j d k mi;k sx Hkh d j ldsx hA
l h0 , l 0l h0 &, l0 i h0 o h0 f= o s.kh l h0 , l 0l h0 &, l0 i h0 o h0 f= o s.kh l h0 , l 0l h0 &, l0 i h0 o h0 f= o s.kh l h0 , l 0l h0 &, l0 i h0 o h0 f= o s.kh (C.S.C.-S.P.V. TRIVENI
Hkkj r lj d kj ds bysDV ªkfu d ,oa l wpu k iz ks| kSfxd h foHkkx u s t u l q fo/kk d sUnz ksa d h ;kst u k d ks xz keksa ,oa “kgj h { ks=ksa d s okM ksZ a rd igq Wapku s gsr q l h0 ,l0 l h0 &
f=os.kh d sUn z ksa d ks [ kksyu s g s r q ;g ;kst u k “kq: d h gSA bl ;kst u k ds vUr xZ r Hkkj r lj d kj l h/ks lHkh ,oa “ kgj h { ks=ksa d s okM ksZ a rd “kkld h; ,oa vU; l q fo/kkvksa d ks ,d gh dsUn z ij
miyC/k d j ku k pkgr h gSA bl ;kst u k ds vUr xZ r iz R;sd xz ke iapk;r ,oa “kgj h { ks= d s iz R;sd okMZ esa [ kksyk t k;sxkA l EcfU/kr xz ke iapk;r ;k okM Z d s csj kstxkj fcu k fdl h t ekur
j kf”k fn ;s ;g d sUn z [ kksy ldrs gS aA l h0 ,l0 l h0 &,l0 ih0 oh0 f=os.kh t ks fd bysDV ªkfu d ,oa l wpu k kkx ds vUr xZr d k;Z dj j gk gS og j k’V ªh; l wpu k foK ku dsUn z ¼,u 0 vkbZ0l h0 ½ d h ft yk
bu dsUn z ksa d s [ kksyu s e sa lg ;ksx d j sxkA
t u in esa l h0 ,l0 l h0 &,l0 ih0 oh0 f=os.kh d sUnz [ kksyu s gsr q j k’V ªh; lwpuk foK ku dsUnz kr d k;kZ y; esa vkosn u fd ;k t k ldr k gSA ;kst u k ds ckj s esa vf/kd
ls iz kIr d h t k ldr h gS ,oa vkosn u gsr q fu/kkZ fj r iz k: i bykgkckn
llahabad.nic.in ls M kmu yksM fd ;k t k ldr k gSA
l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z [ kksyu s gsr q fu /kkZ fj r ik=r k&[ kksyu s gsr q fu /kkZ fj r ik=r k&[ kksyu s gsr q fu /kkZ fj r ik=r k&[ kksyu s gsr q fu /kkZ fj r ik=r k&
vkon sd lEcfU/kr xz ke iapk;r ;k okM Z d k fu okl h gksu k pkfg;sA vkosn d d e ls d e 1 0 oha ikl ,oa ml s d EI;wV j d k K ku gksu k pkfg;sA efgyk vkosn d d ks iz Fke oj h;r k n h t k;sxhA vu q lwfpr t kfr @tut kfr d s vkosn d ksa d ks oj h;r k nh t k;sxhA
woZ esa ml xz ke iapk;r esa d ksbZ l h0 ,l0l h0 d sUnz d k;Z d j j gk gS r ks n wl j k dsUn z [ kksyu s d h vu q efr u gha n h t k;sxhA vkosn d ds ikl iSu ] vk/kkj@bZ fid d ksM Z gksu k pkfg;sA
l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z [ kksyu s gsr q vko”;d mid j .k &l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z [ kksyu s gsr q vko”;d mid j .k &l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z [ kksyu s gsr q vko”;d mid j .k &l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z [ kksyu s gsr q vko”;d mid j .k &
d sUnz [ kksyu s gsr q d e l s d e ,d ySiV ki@MsLdV ki] fiz UVj ] Ld Suj ] fM ft V y dSej k ,oa ;w0 ih0 ,l0 @bUoVZ j gksu k vko”;d gSA bu lHkh mid j .kksa d k vkon sd d ks Lo;a O;oLFkk d j u h gksxhA
l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z ksa d s vUr xZr n h t ku s o kyh l q fo/k k;sa&l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z ksa d s vUr xZr n h t ku s o kyh l q fo/k k;sa&l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z ksa d s vUr xZr n h t ku s o kyh l q fo/k k;sa&l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh d sUn z ksa d s vUr xZr n h t ku s o kyh l q fo/k k;sa&
eq [;r % feu h cSad ksa d h l q fo/kk] lHkh d Eifu ;ksa d s bU”;ksjsal Ld he] U;w isa”ku Ld he] vk/kkj d kM Z cu k;k t ku k] iSu d kMZ ds fy;s vkosn u ] jsyos fV d V ] ikliksV Z d s fy, vkosn u ] eksckby o M hV h,p fj pkt Z d s l kFk N k=ksa d h vku ykbu i<+kbZ ] V ªsu o cl esa l hV d k vkj { k.k
j kT ; l jd kj } kj k n h t kus okyh l q fo/kk,a Hkh bu dsUn z ksa ij miyC/k d jk;h t k;saxhA
;kst u k ds ckj s e sa t ku d kj h r gl hy ,oa O ykd f LFkr L oku dsUn z ksa l s iz kIr d h t k ld r h gSA;kst u k ds ckj s e sa t ku d kj h r gl hy ,oa O ykd f LFkr L oku dsUn z ksa l s iz kIr d h t k ld r h gSA;kst u k ds ckj s e sa t ku d kj h r gl hy ,oa O ykd f LFkr L oku dsUn z ksa l s iz kIr d h t k ld r h gSA;kst u k ds ckj s e sa t ku d kj h r gl hy ,oa O ykd f LFkr L oku dsUn z ksa l s iz kIr d h t k ld r h gSA
l h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh fu Eu cSu j d k mi;k sx Hkh d j ldsx hAl h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh fu Eu cSu j d k mi;k sx Hkh d j ldsx hAl h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh fu Eu cSu j d k mi;k sx Hkh d j ldsx hAl h0 ,l0l h0 & ,l0 ih0 oh0 f=o s.kh fu Eu cSu j d k mi;k sx Hkh d j ldsx hA
S.P.V. TRIVENI)
Hkkj r lj d kj ds bysDV ªkfu d ,oa l wpu k iz ks| kSfxd h foHkkx u s t u l q fo/kk d sUnz ksa d h ;kst u k d ks igq Wapku s gsr q l h0 ,l0 l h0 &,l0 ih0 oh0
f=os.kh d sUn z ksa d ks [ kksyu s g s r q ;g ;kst u k “kq: d h gSA bl ;kst u k ds vUr xZ r Hkkj r lj d kj l h/ks lHkh ,oa “ kgj h { ks=ksa d s okM ksZ a rd “kkld h; ,oa vU; l q fo/kkvksa d ks ,d gh dsUn z ij
R;sd xz ke iapk;r ,oa “kgj h { ks= d s iz R;sd okMZ esa EcfU/kr xz ke iapk;r ;k okM Z d s csj kstxkj fcu k fdl h t ekur
t ks fd bysDV ªkfu d ,oa l wpu k kkx ds vUr xZr d k;Z dj j gk gS og j k’V ªh; l wpu k foK ku dsUn z ¼,u 0 vkbZ0l h0 ½ d h ft yk
t u in esa l h0 ,l0 l h0 &,l0 ih0 oh0 f=os.kh d sUnz [ kksyu s gsr q j k’V ªh; lwpuk foK ku dsUnz kr d k;kZ y; esa vkosn u fd ;k t k ldr k gSA ;kst u k ds ckj s esa vf/kd
vkosn u gsr q fu/kkZ fj r iz k: i bykgkckn
woZ esa ml xz ke iapk;r esa d ksbZ l h0 ,l0l h0 d sUnz d k;Z d j j gk gS r ks n wl j k dsUn z [ kksyu s
] fiz UVj ] Ld Suj ] fM ft V y dSej k ,oa vkon sd d ks Lo;a O;oLFkk d j u h gksxhA
;ksjsal Ld he] U;w isa”ku ikliksV Z d s fy, vkosn u ]
eksckby o M hV h,p fj pkt Z d s l kFk N k=ksa d h vku ykbu i<+kbZ ] V ªsu o cl esa l hV d k vkj { k.kA vkxkeh j kT ; l jd kj } kj k n h t kus okyh l q fo/kk,a Hkh bu dsUn z ksa ij miyC/k d jk;h t k;saxhA
;kst u k ds ckj s e sa t ku d kj h r gl hy ,oa O ykd f LFkr L oku dsUn z ksa l s iz kIr d h t k ld r h gSA;kst u k ds ckj s e sa t ku d kj h r gl hy ,oa O ykd f LFkr L oku dsUn z ksa l s iz kIr d h t k ld r h gSA;kst u k ds ckj s e sa t ku d kj h r gl hy ,oa O ykd f LFkr L oku dsUn z ksa l s iz kIr d h t k ld r h gSA;kst u k ds ckj s e sa t ku d kj h r gl hy ,oa O ykd f LFkr L oku dsUn z ksa l s iz kIr d h t k ld r h gSA
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L k h0, l0 lh0&, l0i h0 ohL k h0, l0 lh0&, l0i h0 ohL k h0, l0 lh0&, l0i h0 ohL k h0, l0 lh0&, l0i h0 oh 0 ] ¼f =os .kh½ Hkkjr lj dkj0 ] ¼f =os .kh½ Hkkjr lj dkj0 ] ¼f =os .kh½ Hkkjr lj dkj0 ] ¼f =os .kh½ Hkkjr lj dkj
Ds Ds Ds Ds v ar Zx rv ar Zx rv ar Zx rv ar Zx r
f=f=f=f= os.khos.khos.khos.kh l sok dsUn zl sok dsUn zl sok dsUn zl sok dsUn z
e q> s ,d c kj i z; ksx d js] f Qj t ho u Hk j dh n ksL rhe q> s ,d c kj i z; ksx d js] f Qj t ho u Hk j dh n ksL rhe q> s ,d c kj i z; ksx d js] f Qj t ho u Hk j dh n ksL rhe q> s ,d c kj i z; ksx d js] f Qj t ho u Hk j dh n ksL rh
i Su dkMZ c uo k;s
vk/kkj dkMZ c uo k;s
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l jkdjh c Sad esa i Sl s tek@fudklh djsa
leL r vkuy kb u QkeZ
lH kh fjtY V fudyo k;sa
vk;@tkfr@fu o kl i zek.k i= cuo k;s
, y 0vkb Z0lh0 dh fdL r tek
djsa
E k= 3 #i ;sesa [ ksrh dh lHkh
tkudkjh i zkIr djsaA
E ksc kb y fjpktZ djo k;saA
V h0oh0 fMLdjhpktZ
i kliksV Z ds fy ;sQkeZH kjsaA
i rk%&o h0, y0b Z0 d k i rk e ksc kb y&
fdlh Hkh tkudkjh ds fy ;s e ksckby ij dky djs aA& 9999999999
l ekxe
l j d kj ] u kxfj d lso k;sa , o a O ;o l k;h