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Unformatted text preview: 308n2?3 Princigles of Assembly La}: guag es: BaoZean Zogic. I Negation (NOT): «A ‘ 0r )1
Conjunction (AND): A&B er AAB 0: AB Disjunctien (OR); A13 01* AVE or A+B 308~273 Principles 0f Assembi’y Languages. Boolean logic. Representing Boolean values as electrical current. V true, I false, 0 NOT:
5\
A “9—41 AND: A ::D—A&B B OR: (a) 3053273 Princi £85 {#:4333me Lan sea es. Baolean 20 i6. 3 308223 Princégies 0f Assembly Language/‘58 Baalean iagic. 4 Laws {)f 300162311 algebra. Tautolagy law: AI~AzZ
Contradiction law: A&~A=0
Commutative laws: F IG 2 GIF
F&G=G&F
Associative laws: (FIGNH z FMGIH) (F&G)&H : F&(G&H} Distributive laws: F1(G&H) = (F!G)&(FlH)
F&(GEH) : (F&G)I(F&H) De Morganis laws: ~(FSG) : ~F&~G
~(F&G} :: ~FE~G Doable negation law: ~(~A}=A 308413 Priacz‘glgs ongsemey Lan Elgages. Boaiean Zagic. 5 XI(X&Y)
(X&])1(X&Y) ,QXXHY)
123‘ X Thus: XF(X&Y):X XI((~X)&Y)
(X1~X)&(X! Y)
1&(XIY)
XiY Thug: XI((~X)&Y):(XEY) 308273 Priecigles af‘Assemblg Languages. Badger: logie. 6 Disjunctive nermal fem: » else called SigmaefPmdzicts farm:
disjuneted set of eenjuneted literals? where a literal is either a Beelean variable 01: its negatieii: e.g.: A&B&(~C}l (~A)&B 2 C Algebraic transformation into Disjunctive normal form. 0 Use De Morgan’s laws and the double negation law to bring the negations immediately before the atoms. 0 Repeatedly use the distributive laws to distribute disjunctions (0R3) ever conjunctiens (ANDS). ~(Al8)&(~(C&D)}
~A&~B&(~CE~D}
~A&~B&~C ! ~A&~B&~D 308423 Pringigigs afASSembly Languages. Badgém logic. 7 Transformation into Disjunctive normal form using truth tables. ' (~A)&(~B) A&(~B} l (~A)&(~B) 30822? Prineipies afﬁssgmbly Languages; Boolean 20356. 8 Algebraic circuit optimisation. &(~3 s {~25 352.5%; i
l “I 11 (A1(~A))&(~B) (1)&(~B) ~B 3&8273 PringipZes QfAssgmbly Languages. 80638:??? Zagic. 9 Transfer intt} Disjuactive normal form:
(A&B&C) IA&(~B)&(~(~A&~C))
Use De Morgan’s laws:
(A&B&C) !A&(~B)&(~~A!~~C)
(A&B&C) IA&(~B)&(AIC)
Use distributive laws: (A&B&C) } (A&(~B)&A) I (A&(~B}&C) Simpliﬁcation:
(A&B&C) i {A&(~B}) I (A&(~B}&C}
{A&C&(Bi~B)}i (A&(~B}}
Aé’zCé’zl I (A&(~B)}
A&C i A&(~B} A&(Cl(~B}) I 308273 Princigles GfAssembiy Langmggs. Cémguting cirmiis. ; Building a Binary Adder. A binary addition Where both A and B are either 0 or I .
C15 2A +8 Where C stands for “Carry” and S stands for “Sum’ﬁ S={~A&B)1(A&~B) C =Ac§B 388273 Prirzcigles 0fASSémey Languages. Comgtgting Circuits. 2 Exclusive 0R. (~A&B) i (A&~B) : [1% Half Adder. 308:2?3 Princigles ofAssemblz languages. Campating circuits. 3 Building a Fall Adder. stzA+B+g Where C stands for “Carry out”, z: stands for “Carry in” and 5
stands for “Sum”. wah«QQQQ‘ 52~A&~B&C I ~A&B&~Q i A&~B&~C £146:chch C=~A&B&€ ! A&~B&c i A&B&~c i A&B&C 308473 Prézzcigiés OfAssembly Languages. 4 Cgmgutz'ng Circuits. 4 Sum. ~:4&~B&C i ~A&B&~€: I A&~B&~c 1 [462.8626 ~A&(~B&c l B&~C) EA&(~B&~C ! 3&6) mm, W vy‘” ~A&(B$C) 1A&(~~(~B&~C l 3&6»
"2462(356) IA&(~(~(~B&~C) & ~(B&C)))
~A&(B§éc) lA&(~((~~BI~~C)&(~BI~C))) ~A&(B§C) i A&(~ ((§162w&(~§:£2) ~A&(B§zc) IA&(~(B&~B i C&~B E B&~C I C&~C))
~A&(B%%C) IA&(~(01 C&~B !B&~C i 0))
~A&(B§§C) {A&~(B%C} Agrt’Béc} 3084393 Princigies c3fAssemey Languagex Camgufirzg Cif‘ii‘iiiZS. 3 Carry. ~A&B&c iA&~B&C iA&B&~C iA&B&C B&c&(~AIA) IA&C&(~BIB) I A&B&(~clc)
B&c&l 1A&C&Z IA&B&1 8&6 lAcS’zCWAé’zB 3084,73 Princi les 0fAssemey Laﬁguaves. Com wing sircaits. 6 Full Adder. 308—273 Princigies afAssembfy Languagés. Camgutirzg Circuits. 7 4bit Adder. FA
B2 !
A 52
" FA ‘
B3 ;
A4 : Si
84 E ,,,,,,,,,,,,,, C 308873 Priszci [es 0 ﬁssemeyLanguages. Cam grin Cirwirs. 8 Memory. State RS FlipFlop. 368~273 Princigles of Assembly Languages. Comgming circuits. 9 0 I 0 I ...
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