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4844 Sq—————-Boo Dean function __Representaction Sop & Pos -prm _ wr Se —= _ Red ee . Ts ~» — 3 tp Digital electanicrs if we have Dene catnt then SEs cutee inthe finction the digit’ —_inpuls. = The Yelatinship _blw the inp quel aw At canbe thes using fhe _“Tith table cy Brolean expression. The Boolean _edpvession oy the Beollean function exthey in tye o} SoP = Sum e} Py educt rs POS s Reduct ¢} som ~@——_SOP :- ~G Sum o} Pedeel five Representection te 4tn_— SoP Te Proclot tem the Legical AND eperation > _ 4 Aifforent bli _ Vaviabte unl be in Tree Jorn. i) Complemented form Product — Logical AND OPera tion (&} CamScanner lolelelddddaleen Example. o} Procbuct eum t- A.B A-B-c _ A.8 2 th A.B Beth _vaviable ave in Tue form 25a ABC A& Care in Wwe firm and ais __B ia n___ complement foun = ty ABA tin te Tre een “while 2 Bs wa the complement foo Sum — Logica? me) oR operation Piz ip Pp 5, SS oP forme] expression. _Diffexent Produck fon terms ave. Detizally ORed TREPEREPREER RP? cs Q iS 3 Da q 8 5 5 e 2 q r = Lamp Ue eh. surn__ ees g- (A+B) : (A+Btc) : (A+B) Sh___ Pos -fevm Different sum tewms are Qogicaly ANDed { a. eS i’ shen enleeatat “ (Ax8). (A+B+c) . (A+B) } a predwct Product _ E, (A.Bic) = (A+8). (4+ Bre). (B+T) & (AB.c.0) = (R+0)» (4+B8+0)- (Arc) Canonicod m Pos Non = Ganenicnd Foxna AR nen-canenical fon each sum tex ton oma not COutnin a00 the vorishle _.} the function eg Fy Fede So. _Cancnical frum, each sum teu cacbun alld the Variable ra the Function: e-4, Ff, (A,8) = (A+®8). (A+B). (A+x8) @ «cf 02 ee eo me Be ee BD em fC lm le le lien le cs Q iS 3 Da te} 8 5 5 oQ 2 a Mintem ‘ Ns Ne Ss ys . _— Ji — Canonical SoP foun, each —_p radwck teum ys alas called mute, til ” >» » 3 aparereome —F.f.8.c)2 A.B.C C+ ABC +A. Bc ee Se, ee ese yo Me Canonical Sof. foun _c)—tepresendadion is alge Sad to be se pi arin ee ae > 4, Cansmicgl Pos fou my each gum tern tb MP ads caer! aati. = Be me As) = (Ar). (Ae). (AG a) _ mo a } t t at ~@— _ — Maaterm, Mayhem ax tena . at intoms ave the complement of tlaxtern yi = ©, ~ (&} CamScanner : variables | A B c. Mintems fay oO oO ABC Mo (3) ( ABC Mm, 2) \ o _ABE mM, © \ | ABC m3 \ ) ° ABC Mu l © \ ABC ws | \ 2 ABS We / \ | \ ABC m3 _Feoy 3 inputs AMheve aye. Aetna A mintewns B= A Sm __ General for ow input variable Aheve aye 2 into ms. oF l ; ; uth 4abl 2 s 0 A iNew + H expversion _in the fo +m °} mivcdevms, = Sh we wank to write the algebyic few __o} Ane Junckion pai 00 write ald te mintenn Contes Peaclina do nase crmbinaton ¥ox which he _outbut =) _ Then Legend tis OR ath these teams - pp! ® A wR nn oo assess re eee _ 2 0. ee oe _ ba ° = Lac escicl me snial _ _ 4 a. ee eee SS) — _ } Is t | | | | | | | | a 2 ® = oleae blialn the sum feu which cena of a a * 7 : _ | For functions with __“n input _vayrabbes _theve aye 2 vnaxterms: (&} CamScanner —— Hie hase _gi iven _-tveth table then haw +o “a a ml a its output in the form 0} _maxtems? | A is} an oF EF, 6! - 2 ° 2) 4 ° 2 Q \ ° | fe) | (2) 4 ° © J jot | | \ ie) ° 4. oO \ © \ ° \ \ \ o fo) | i | I 4. (e) Fist find 6" which ts Repyésent F." in the __fovim e}___sum__o}_minteawn Fiz ABc + fac + ABC+ ABE Taking Complemert of ony —_Fi= Ac + ABc+ ABC + ARC By De Miovajan's Law —=— = 7 ~ = (a) YU Fy = ABC ARC» ABC + ABC Again C= (Ax B+7). (Ax B+E). (Ar BtE)- (At Be) f= (A+ 8+), (at@+et), Arete). CA+Bsc) Dy E az M4,. M4, his. Ie Hs Fy mW (1, 3,5) 6) Hws T S@et_seeornnve bo w go ® im \mla!al a! a! =! al ol! a! cs Q ss 3 Da te} 8 5 5 e 2 Conversions £, (A,B,C) = J. (245,69 Canonical SoP Ferm Ae Mtoe P14. Py hy Fre am (0,3,4,2) Canonical POS form : Fue 2(0,2,4, 4) 5 Canenical oP fav i B= £C1,3.8,6) Bb Fi mye matmcam, : Re My Ms ty ‘ £, = im, . my. Me | Fae 2 PPE PP a Pa 2 Comninnd POS foun. = SEEEEEEEEEeeene r (&} CamScanner 
