MELJUN CORTES Logic Gates Examples

8/8/2019 MELJUN CORTES Logic Gates Examples

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Design a circuit that will evaluate the expression

F = AB’ + A

Will there be an alternative simpler solution tothe above function?

Logic Gates Examples * Property of STI

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Solution:

Recall from Theorem 6a that:

X +XY = (1+Y )X = (1)X = X

let X = A and Y = B

Applying this to our expression, we get:

F = AB’ + A = A(B’ + 1) = A(1) = A


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Circuit implementation of the function

F = A(B’+1)


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Take a look at the circuit below and directlyderive the Boolean expression from it. Attempt

to implement a new circuit that does the samething as the old one but uses less components.


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Solution:


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Solution (cont.):


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Solution (cont.):

The expression, therefore:

F = {[B(A+B)’](A+C)’}’ 6. Theorem 5 [De Morgan’s]: (XY)’ = X’+Y’

F = [B(A+B)’]’ + (A+C)’’

F = B’ + (A+B)’’ + (A+C)’’

’ ’


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. =

F = B’ + (A+B)’’ + (A+C) F = B’ + (A+B) + (A+C)


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Solution (cont.):

8. Regroup the terms:

F = (A+A) + (B+B’) + C

9. Theorem 1a: X + X = X

F = A + (B+B’) + C

10. Postulate 6: A + A’ = 1

F = A + 1 + C 11. Theorem 2a: X + 1 = 1

F = 1


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expression above would be:


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How many terms and literals do the followingcircuits have? Manipulate and simplify the

expressions if needed.

Solution:

2-terms: AB and C’

literals: A, B , C’


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Boolean expression:

F = AB + C’


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Solution:

2-terms: (A+B)’ and CC’

literals: A’ , B’ , C , C’

Boolean expression:

’ ’


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= + +

De Morgan’s Theorem:F = (A’B’) + CC’

F = (A’B’) + 0

F = (A’B’)

F = A’B’ or (A+B)’


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Solution:

3-terms: (A+B)’ , ((A+B)’B)’ , and (C+D)’

literals: A’ , B’ , C’ , D’

F = ((A+B)’B)’(C+D)’

’’ ’ ’


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= + + +

= ((A+B)+B’)(C’D’) = (A+(B+B’))(C’D’)

= (A+1)(C’D’)

= 1(C’D’)

F = (C+D)’


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Enumerate the number of terms and literals forthe following Boolean expressions and draw

their logic diagram.

1) F = (A’+B )C

2) F = A’B ’C ’

3) F = A’B + AC

4) F = AC + A’BC + A’BC ’5) F = AB ’ + A’B

Solution:

1. 2-terms: A’+B and A’+B C


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literals: A’ , B , C


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Solution (cont.):

2. 1-term: A’B’C’

literals: A’ , B’ , C’


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Solution (cont.):

3. 2-terms: A’B and AC

literals: A’ , B , A, C

4. 3-terms: AC , A’BC , and A’BC’

’ ’


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, , , ,


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Solution (cont.):

5. 2-terms: AB’ and A’B

literals: A’ , A, B’ , B


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You have been accepted as an intern at DurianTech’s Reverse Engineering Department. The

department where you are assigned is trying toexamine some digital circuits used in thecellular phones of its competitor, BananaTelecoms. Your first task as a cadet reverseengineer is to find out what each of the followingcircuits does. You need to get the functional

characteristics of the circuits by examining their

logic diagrams. Determine the Booleanexpression of each logic diagram and obtainits truth table.


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The lead engineer in your department said thathe needs to implement the circuit shown below.

However, there has been a shortage in four-input NAND gates in the supply bin and the onlyavailable gates are two-input OR and NOR. Hesays that he vaguely remembers a method tomake a similar circuit using identities andHuntington’s postulates on the circuit’s Boolean

expression. He asks you if there is a possibility

that the circuit can be implemented using onlytwo-input OR and NOR gates.


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MELJUN CORTES Logic Gates Examples

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