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+19 votes

What is the minimum number of gates required to implement the Boolean function $\text{(AB+C)}$ if we have to use only $2\text{-input NOR}$ gates?

  1. $2$
  2. $3$
  3. $4$
  4. $5$
asked in Digital Logic by Veteran (59.5k points)
edited by | 4.3k views

5 Answers

+45 votes
Best answer

Given boolean function is 

 f$ = AB + C$

   $= (A+C) . (B +C)$ 

   $=((A+C)' +(B+C)')'$

Therefore, $3$ NOR gate required .

answered by Loyal (6k points)
edited by
+5 votes
Answer should be 3 nor gates...A.B + C can be written as (A+C).(B+C) which is a OR-AND realization and can be made with 3 NOR gates as OR- AND is similar to a NOR-NOR realization...
answered by (71 points)
edited by
+2 votes

Option : B 


answered by (57 points)
+1 vote

Almost same solution,

answered by Loyal (5.3k points)
0 votes
answer - D

AB + C = ((AB + C)')' = ((AB)'C')' = ((A' + B')C')' = (A' + B')' + C

two NOR gates for complementing A and B

one for computing (A' + B')'

one to compute ((A' + B')' + C)'

one to negate the last result
answered by Loyal (9k points)

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