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Electronic Labs_5 - 26-4 Boolean Algebra w A B C.A_l.‘.£...

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Unformatted text preview: 26-4 Boolean Algebra w A+B+C+ .A;_l?..‘.£;.-. =X-E-E- A-B-C- list-.21.»..- 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 4-1 of Laboratory Exercise 4. Exercise Procedure D 3. a) Connect the two circuits shown in Fig. 26-5. Use the Switches and LED Displays for the inputs and outputs. Turn on the trainer power and complete Table 26-1. l \ , 7400 To ! . A I ‘ FROM . — 1 I‘sWITCH BE— A'3 0'5”“ J i I la} _ _ T0 A+B DISPLAY {bl Fig. 26-5 ——| __—_l ---—fllfl ME].- na— EIIII- III- .EI- I'll“ Table 26-1 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. 26-6. Use the Switches and LED Displays for the inputs and outputs. Turn on the trainer power and com- plete Table 26-2. 7402 7 TO A . H ‘ n FROM . p AY SWITCH {Em—KM}! Dis L to: to 3-5 DIsnLAr' _ mg, A . 1:2. It: A111. :L‘ if. —_ _-__l I—I—III Ian- III- “I.“ III“ III!“ III- II“ I.“ Table 26-2 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. 26-7. The equation is X=(A+BC)(AC+BD). D b)Write the Boolean equation for the circuit shown in Fig. 26-8. The equation is“ X=(A+BC)+(AC+BD). ...
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