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What is the minimum number of gates required to implement the Boolean function (AB+C) if we have to use only 2-input NOR gates?
- a)2
- b)3
- c)4
- d)5
Correct answer is option 'B'. Can you explain this answer?
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What is the minimum number of gates required to implement the Boolean ...
given boolean function is
f = AB + C
= (A+C) . (B +C)
=((A+C)' +(B+C)')'
f = AB + C
= (A+C) . (B +C)
=((A+C)' +(B+C)')'
therefore 3 NOR gate required .
Most Upvoted Answer
What is the minimum number of gates required to implement the Boolean ...
Solution:
Given Boolean function is (AB C), which can be expressed as (A NOR B) NOR C.
We need to implement this using only 2-input NOR gates.
Steps to implement the given function:
Step 1: Obtain the NOR expression for (A NOR B) as (A NOR B).
Step 2: Obtain the NOR expression for ((A NOR B) NOR C) as ((A NOR B) NOR C).
Step 3: Implement the NOR gate expression obtained in step 1 using two 2-input NOR gates.
Step 4: Implement the NOR gate expression obtained in step 2 using three 2-input NOR gates.
Therefore, the minimum number of gates required to implement the given Boolean function using only 2-input NOR gates is 3.
Hence, option B is the correct answer.
Given Boolean function is (AB C), which can be expressed as (A NOR B) NOR C.
We need to implement this using only 2-input NOR gates.
Steps to implement the given function:
Step 1: Obtain the NOR expression for (A NOR B) as (A NOR B).
Step 2: Obtain the NOR expression for ((A NOR B) NOR C) as ((A NOR B) NOR C).
Step 3: Implement the NOR gate expression obtained in step 1 using two 2-input NOR gates.
Step 4: Implement the NOR gate expression obtained in step 2 using three 2-input NOR gates.
Therefore, the minimum number of gates required to implement the given Boolean function using only 2-input NOR gates is 3.
Hence, option B is the correct answer.
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