Unformatted text preview: (Amiga ~63 +1—(Evb) Fig. 263 8/ 2. a)Re‘ferring to the output _of_ the circuit
of Fig. 263 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. 263. (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)] =(B1+AB+BC)+AC [Group B terms (Associative
Law)] Boolean Algebra 263 =‘Bl(rlj+A’+C')ﬂAC [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. 264 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. 264 C! d) Compare the circuits of Fig. 263 and
264. 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) AB=A+B For any number of variables, the theorems take
the form: ...
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 Fall '05
 Myer,B

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