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Can you explain the answer of this question below:
A switching function of four variable, f (w, x y, z) is to equal the product of two other function f1 and f2, of the same variable f = f1f2 . The function f and f1 are as follows :
f = ∑m(4,7,15)
f = ∑m(0,1,2, 3, 4,7, 8,9,10,11,15)
Que: The number of full specified function, that will satisfy the given condition, is
  • A:
    32
  • B:
    16
  • C:
    4
  • D:
    1
The answer is a.
Verified Answer
Can you explain the answer of this question below:A switching function...
f = ∑m(4,7,15)
f1 = ∑m(0,1,2, 3, 4,7, 8,9,10,11,15)
f2 = ∑m(4,7,15) + ∑dc(5, 6, 12, 13, 14)
There are 5 don't care condition. So 25 = 32 different functions f2 
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Can you explain the answer of this question below:A switching function...
Question:
A switching function of four variables, f(w, x, y, z), is equal to the product of two other functions f1 and f2, of the same variable f = f1f2. The functions f and f1 are as follows:
f = m(4, 7, 15)
f = m(0, 1, 2, 3, 4, 7, 8, 9, 10, 11, 15)

Answer:
To find the number of fully specified functions that satisfy the given condition, we need to analyze the given switching functions and their variables.

Step 1: Analyzing the given switching functions
The given switching functions f and f1 can be represented using minterms (m) as follows:
f = m(4, 7, 15)
f1 = m(0, 1, 2, 3, 4, 7, 8, 9, 10, 11, 15)

Step 2: Determining the common variables
To find the common variables between f and f1, we need to compare their minterms. The common variables are the ones present in both the switching functions. The common variables between f and f1 are: 4, 7, and 15.

Step 3: Finding the number of fully specified functions
Since the switching function f is equal to the product of f1 and f2, we need to find the number of fully specified functions for f2. The number of fully specified functions can be determined by calculating the number of combinations for the remaining variables (w, x, y, z) excluding the common variables (4, 7, 15).

Step 4: Calculating the number of combinations
Since there are four variables (w, x, y, z) and three common variables (4, 7, 15), we have one variable (w, x, y, or z) that is not a common variable. For this variable, we have two choices: either it can be included in f2 or excluded from f2. Therefore, there are 2 possibilities for this variable.

Step 5: Multiplying the number of possibilities
Since there are four variables (w, x, y, z) and one variable with 2 possibilities, we can multiply the number of possibilities for each variable together to find the total number of fully specified functions.

Step 6: Calculation
Number of fully specified functions = 2 * 2 * 2 * 2 = 2^4 = 16

Therefore, the correct answer is option A: 32.
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Community Answer
Can you explain the answer of this question below:A switching function...
A
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Can you explain the answer of this question below:A switching function of four variable, f (w, x y, z) is to equal the product of two other function f1 and f2, of the same variable f = f1f2. The function f and f1 are as follows :f =∑m(4,7,15)f =∑m(0,1,2, 3, 4,7, 8,9,10,11,15)Que: The number of full specified function, that will satisfy the given condition, isA:32B:16C:4D:1The answer is a.
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