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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? (Answer up to the nearest integer)
Correct answer is '3'. Can you explain this answer?
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What is the minimum number of gates required to implement the Boolean...
AB + C = (A + C)(B + C) = ((A + C)' + (B + C)')'
So, '3' 2-input NOR gates are required.
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What is the minimum number of gates required to implement the Boolean...
Explanation:
Minimum Number of Gates Calculation:
- The given Boolean function is (AB + C).
- We need to implement this function using only 2-input NOR gates.
- Let's first simplify the given function:
- (AB + C) = (AB + C + CC) [Adding a redundant term]
= (AB + C(1 + C)) [Applying Distributive Law]
= (AB + C) [C(1 + C) is always equal to C]
Implementation Using NOR Gates:
- The simplified function (AB + C) can be implemented using the following steps:
1. Implementing the term C using a NOR gate: C = NOR(C, C) = C'
2. Implementing the term AB using a NOR gate: AB = NOR(A', B')
3. Implementing the final function (AB + C) using a NOR gate: (AB + C) = NOR(AB, C)
Minimum Number of Gates:
- The implementation requires a total of 3 NOR gates to realize the Boolean function (AB + C).
- Therefore, the minimum number of gates required is 3 to implement the given Boolean function.
Minimum Number of Gates Calculation:
- The given Boolean function is (AB + C).
- We need to implement this function using only 2-input NOR gates.
- Let's first simplify the given function:
- (AB + C) = (AB + C + CC) [Adding a redundant term]
= (AB + C(1 + C)) [Applying Distributive Law]
= (AB + C) [C(1 + C) is always equal to C]
Implementation Using NOR Gates:
- The simplified function (AB + C) can be implemented using the following steps:
1. Implementing the term C using a NOR gate: C = NOR(C, C) = C'
2. Implementing the term AB using a NOR gate: AB = NOR(A', B')
3. Implementing the final function (AB + C) using a NOR gate: (AB + C) = NOR(AB, C)
Minimum Number of Gates:
- The implementation requires a total of 3 NOR gates to realize the Boolean function (AB + C).
- Therefore, the minimum number of gates required is 3 to implement the given Boolean function.
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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? (Answer up to the nearest integer)Correct answer is '3'. Can you explain this answer?
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