Show that the Boolean function, f = A ⊕ B ⊕ AB between two variables, A and B, can be implemented using a single two-input gate.
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Step 1
First, we need to simplify the Boolean function f = A ⊕ B ⊕ AB using Boolean algebra rules. f = A ⊕ B ⊕ AB = A ⊕ B ⊕ A(B + 1) (distributive law) = A ⊕ B ⊕ AB + A (distributive law) = A(1 ⊕ B) ⊕ B ⊕ AB (factoring out A) = A'B ⊕ B ⊕ AB (complement law) = A'B ⊕ Show more…
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