Consider the following Boolean function of four variables: f(w,x,y,z) =…

Solution summary: determine which variables are irrelevant and simplify the function.

Write the given minterms in binary (w x y z):

• 1 = 0001, 3 = 0011, 4 = 0100, 6 = 0110, 9 = 1001, 11 = 1011, 12 = 1100, 14 = 1110

Identify variables that do not affect f:

• w is irrelevant because each minterm appears with w=0 and with w=1: (0001,1001), (0011,1011), (0100,1100), (0110,1110).

• y is irrelevant because each minterm appears with y=0 and with y=1: (0001,0011), (1001,1011), (0100,0110), (1100,1110).

Reduce the function to depend only on x and z and evaluate its truth table:

• For x=0, z=0 none of the minterms (0,2,8,10) are included → output 0.

• For x=0, z=1 all minterms (1,3,9,11) are included → output 1.

• For x=1, z=0 all minterms (4,6,12,14) are included → output 1.

• For x=1, z=1 none of the minterms (5,7,13,15) are included → output 0.

Thus the two-variable function in x and z has truth table 0,1,1,0 which is exclusive OR.

Conclusion: the original function is independent of two variables (w and y) and simplifies to f = x XOR z.