Electronic Labs_4

# Electronic Labs_4 - (Amiga ~63 1—(Evb Fig 26-3 8 2...

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Unformatted text preview: (Amiga ~63 +1—(Evb) Fig. 26-3 8/ 2. a)Re‘ferring to the output _of_ the circuit of Fig. 26-3 as ~\.¥=(A+B)(B+C)+A(C+D), is it possible to simplify any part of the equation, and if so, which part? 0 — _ AB...rl:.l\..93§l§l3.ﬂ:§._..i...A§~.._-.LA.D ............ It ispossible to simplify the expression (A+B)(B+C). lE/ b) Simplify the expression (A+B) (B+C) using Boolean algebra and state the ,full simplified equation for the circuit of Fig. 26-3. (A+B)(B+C) =AB+AC+BB+BC [Algebraic expansion (Distrib— ﬁ’ utiue Law)] =AB+A C+B+BC — [BB=B(Identity)] T-‘AB+AC+B(1)+BC [B=B_(r) (Identity ) ] =B(1)+AB+BC+AC [Rearrange terms (Commuta- tive Law)] =(B-1+AB+BC)+AC [Group B terms (Associative Law)] Boolean Algebra 26-3 =‘Bl(rlj+A’+C')ﬂ-AC [Factor out B (Distributive ' ‘ ' Law)] ' eB‘a )‘+AC [B(1+A+C)=B(l ) (Identity)] =B+AC [B(1)=B (Identity)] «’\ Therefore: (A+B)(B+C)+X(5+D)ﬁ§}lflﬁ@z(5+D). [2/ c)Ca.n the circuit of Fig. 26-4 be used to ' iinplement the simpliﬁed logic equation Y=B+AC+' A(C+D)? Xes, the gate o_ut£uts are as follows: gate A is C+D; gate_(,;is A(C+D),' gate B is AC; and gate D is B+A C+A(C +D). Fig. 26-4 C! d) Compare the circuits of Fig. 26-3 and 26-4. How many and what type of logic gates have been eliminated from the circuit by simpli- ﬁcation using Boolean algebra? r'} _ '-_,"‘._ ." C Two OR gates have been eliminated. Objective B. Determine that DeMorgan’s theorems deﬁne the dual gating functions of the basic NAND and NOR gates and verify that these theorems can be applied to complex logic circuits. Preparatory Information. DeMorgan’s theorems re- late to the dual gating functions 'of the basic NAND and NOR gates. This provides a powerful tool in solving Boolean equations since the dual for each function can be substituted directly in an equation for the basic function. Additionally, because the duality exists for gates with any number of inputs, DeMorgan’s theorems are valid for equations with any number of variables and for equations having complex terms that have the basic form. DeMOrgan’s theorems are: (1) A+B=“A‘-}"3' (2) A-B=A+B For any number of variables, the theorems take the form: ...
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