Unformatted text preview: 264 Boolean Algebra w A+B+C+ .A;_l?..‘.£;.. =XEE
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Other variations of DeMorgan ’s theorem are possible by applying the principle of double negation. This
yields: A'B=A___ _ A+B=m=Xv§
These last forms of DeMorgan’s theorems show
their relationship to the duality of the basic AND
and OR gates. This is extremely useful since it
allows conversion from one logic configuration to
another. It also shows that any logic function can
be performed using either NAND or NOR logic
exclusively. These forms are the mathematical
justification for the logic gate equalities shown in
Table 41 of Laboratory Exercise 4. Exercise Procedure D 3. a) Connect the two circuits shown in Fig.
265. Use the Switches and LED Displays for the
inputs and outputs. Turn on the trainer power and
complete Table 261. l \ , 7400 To !
. A I
‘ FROM . — 1
I‘sWITCH BE— A'3 0'5”“
J i
I la} _ _ T0
A+B DISPLAY {bl Fig. 265 ——
__—_l —ﬂlﬂ
ME]. na—
EIIII III
.EI
I'll“ Table 261 C] b) Do the truth tables of step 3 (a) prove
DeMorgan’s first theorem? Yes, the inputs and outputs are identical and hence
the two circuits are functionally the same. D 4. a) Connect the tva circuits of Fig. 266.
Use the Switches and LED Displays for the inputs and outputs. Turn on the trainer power and com
plete Table 262. 7402 7 TO
A . H ‘ n
FROM . p AY
SWITCH {Em—KM}! Dis L to: to
35 DIsnLAr' _ mg, A . 1:2.
It: A111. :L‘ if. —_
___l
I—I—III
Ian III
“I.“ III“
III!“ III
II“ I.“ Table 262 IE/ b)Do the truth tables of step 4 (a) prove
DeMorgan’s second theorem? Yes, the inputs and outputs are identical and hence
the two circuits are functionally the same. [I 5.3)Write the Boolean equation for the
circuit shown in Fig. 267. The equation is X=(A+BC)(AC+BD). D b)Write the Boolean equation for the
circuit shown in Fig. 268. The equation is“ X=(A+BC)+(AC+BD). ...
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 Fall '05
 Myer,B

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