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What is the minimum number of 2-input NOR gates required to implement a 4-variable function expressed in sum-of minterms form as f =∑( 0,1, 5, 7, 8,10,13,15) ? Assume that all the inputs and their complements are available.
Correct answer is '3'. Can you explain this answer?
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What is the minimum number of 2-input NOR gates required to implement ...
f =∑ ( 0, 2, 5, 7,8,10,13,15)
As per the questions their complemented and normal both type of inputs are available.
So,
Their equivalent circuit can be redrawn like.
Therefore, minimum number of NOR-gate = 3.
As per the questions their complemented and normal both type of inputs are available.
So,
Their equivalent circuit can be redrawn like.
Therefore, minimum number of NOR-gate = 3.
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What is the minimum number of 2-input NOR gates required to implement ...
The minimum number of 2-input NOR gates required to implement a 4-variable function expressed in sum-of-minterms form as f = Σ(0, 1, 2, 4, 7, 8, 9, 10, 11, 14) can be found using the Karnaugh map method.
The Karnaugh map for a 4-variable function has 16 cells. Each cell represents a minterm, and the minterms are arranged in a Gray code order.
To find the minimum number of NOR gates required, we need to group adjacent cells containing 1s in the Karnaugh map. Each group represents a product term, and the number of groups determines the number of NOR gates required.
In this case, the Karnaugh map would look like this:
```
\ AB 00 01 11 10
CD
00 0 1 1 0
01 0 0 0 0
11 1 1 1 0
10 0 0 0 0
```
Grouping adjacent cells containing 1s, we can form the following groups:
Group 1: AB'CD'
Group 2: ABC'D'
Group 3: ABCD
These groups represent the product terms in the sum-of-minterms expression.
To implement these product terms using NOR gates, we can use De Morgan's theorem, which states that the complement of a product term can be implemented using NOR gates.
So, the minimum number of NOR gates required is equal to the number of product terms, which is 3 in this case.
Therefore, the minimum number of 2-input NOR gates required to implement the 4-variable function f = Σ(0, 1, 2, 4, 7, 8, 9, 10, 11, 14) is 3.
The Karnaugh map for a 4-variable function has 16 cells. Each cell represents a minterm, and the minterms are arranged in a Gray code order.
To find the minimum number of NOR gates required, we need to group adjacent cells containing 1s in the Karnaugh map. Each group represents a product term, and the number of groups determines the number of NOR gates required.
In this case, the Karnaugh map would look like this:
```
\ AB 00 01 11 10
CD
00 0 1 1 0
01 0 0 0 0
11 1 1 1 0
10 0 0 0 0
```
Grouping adjacent cells containing 1s, we can form the following groups:
Group 1: AB'CD'
Group 2: ABC'D'
Group 3: ABCD
These groups represent the product terms in the sum-of-minterms expression.
To implement these product terms using NOR gates, we can use De Morgan's theorem, which states that the complement of a product term can be implemented using NOR gates.
So, the minimum number of NOR gates required is equal to the number of product terms, which is 3 in this case.
Therefore, the minimum number of 2-input NOR gates required to implement the 4-variable function f = Σ(0, 1, 2, 4, 7, 8, 9, 10, 11, 14) is 3.
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What is the minimum number of 2-input NOR gates required to implement a 4-variable function expressed in sum-of minterms form as f =∑( 0,1, 5, 7, 8,10,13,15) ? Assume that all the inputs and their complements are available.Correct answer is '3'. Can you explain this answer?
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