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The total number of Boolean functions which can be realised with four variables is:
- a)4
- b)17
- c)256
- d)65,536
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The total number of Boolean functions which can be realised with four ...
A Boolean function of 4 variables is a function from a set 24 = 16 of elements (all combinations of 4 variables) to a set of 2 
elements. So, number of such functions will be 216 = 65,536
elements. So, number of such functions will be 216 = 65,536Most Upvoted Answer
The total number of Boolean functions which can be realised with four ...
A Boolean function of 4 variables is a function from a set 24 = 16 of elements (all combinations of 4 variables) to a set of 2 elements. So, number of such functions will be 216 = 65,536
elements. So, number of such functions will be 216 = 65,536Free Test
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The total number of Boolean functions which can be realised with four ...
Total Number of Boolean Functions with Four Variables
To understand how many Boolean functions can be realized with four variables, we first need to grasp the concept of Boolean functions.
Definition of Boolean Functions
- A Boolean function is a function that takes binary inputs (0 and 1) and produces a binary output.
- For 'n' variables, each variable can be either 0 or 1.
Calculating the Input Combinations
- With four variables, each variable can independently be either 0 or 1.
- Therefore, the total number of input combinations is calculated as:
- 2^n = 2^4 = 16 combinations.
Output for Each Combination
- For each of the 16 input combinations, the function can produce an output of either 0 or 1.
- This means that for each combination, there are 2 possible outputs.
Total Number of Functions
- Since there are 16 combinations and each can yield 2 outputs, the total number of Boolean functions can be calculated as:
- 2^(number of combinations) = 2^16.
Final Calculation
- Thus, the total number of Boolean functions that can be realized with four variables is:
- 2^16 = 65,536.
Hence, the correct answer is option 'D' (65,536).
To understand how many Boolean functions can be realized with four variables, we first need to grasp the concept of Boolean functions.
Definition of Boolean Functions
- A Boolean function is a function that takes binary inputs (0 and 1) and produces a binary output.
- For 'n' variables, each variable can be either 0 or 1.
Calculating the Input Combinations
- With four variables, each variable can independently be either 0 or 1.
- Therefore, the total number of input combinations is calculated as:
- 2^n = 2^4 = 16 combinations.
Output for Each Combination
- For each of the 16 input combinations, the function can produce an output of either 0 or 1.
- This means that for each combination, there are 2 possible outputs.
Total Number of Functions
- Since there are 16 combinations and each can yield 2 outputs, the total number of Boolean functions can be calculated as:
- 2^(number of combinations) = 2^16.
Final Calculation
- Thus, the total number of Boolean functions that can be realized with four variables is:
- 2^16 = 65,536.
Hence, the correct answer is option 'D' (65,536).
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The total number of Boolean functions which can be realised with four variables is:a)4b)17c)256d)65,536Correct answer is option 'D'. Can you explain this answer?
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