Correct Option: C. 8
Step-by-Step Explanation:
- Understanding Input Variables:
-
A logic gate with three input variables means that there are three distinct inputs, which we can denote as A, B, and C. Each of these inputs can take on one of two possible values: 0 (false) or 1 (true).
-
Calculating Combinations:
- For each input variable, there are 2 possible states (0 or 1).
-
When you have multiple input variables, the total number of combinations can be calculated using the formula:
[
\text{Total Combinations} = 2^n
]
where ( n ) is the number of input variables.
-
Applying the Formula:
- In this case, since we have 3 input variables (A, B, and C), we substitute ( n = 3 ) into the formula:
[
\text{Total Combinations} = 2^3 = 8
]
-
This means there are 8 different combinations of inputs for the logic gate.
-
Listing the Combinations:
- To visualize this, we can list all the possible combinations of the three inputs:
- 000 (A=0, B=0, C=0)
- 001 (A=0, B=0, C=1)
- 010 (A=0, B=1, C=0)
- 011 (A=0, B=1, C=1)
- 100 (A=1, B=0, C=0)
- 101 (A=1, B=0, C=1)
- 110 (A=1, B=1, C=0)
- 111 (A=1, B=1, C=1)
- Each combination represents a unique state of the inputs to the logic gate.
Why Other Options Are Incorrect:
- Option A: 3
-
This option suggests that there are only 3 combinations. This is incorrect because it does not account for the binary nature of each input variable. Each variable can be either 0 or 1, leading to more combinations than just 3.
-
Option B: 4
-
This option implies that there are 4 combinations. This might be true for a logic gate with only 2 input variables (since ( 2^2 = 4 )), but with 3 input variables, the number of combinations increases to 8.
-
Option D: 12
- This option suggests there are 12 combinations, which is incorrect. The number of combinations grows exponentially with the number of input variables, and for 3 variables, it is limited to 8, not 12.
Revision Summary:
- A logic gate with ( n ) input variables has ( 2^n ) possible combinations.
- For 3 input variables, the total combinations are ( 2^3 = 8 ).
- The combinations represent all possible states of the inputs (0 or 1).
- Understanding the binary nature of inputs is crucial for calculating combinations correctly.