To implement the function f(A,B) = ĀB + (ABB) using only NAND and OR gates, we can follow these steps:
1. Write the Boolean expression for the function:
f(A,B) = ĀB + (ABB)
2. Simplify the expression using De Morgan's laws and Boolean algebra:
f(A,B) = ĀB + ABB
= ĀB + AB
3. Implementing the function using only NAND and OR gates:
We can use the fact that NAND gates can be used to implement any logic gate. First, let's break down the expression into smaller parts:
a) Implementing ĀB:
To implement the complement of A (Ā), we can use a NAND gate with both inputs tied to A. The output of this NAND gate will be Ā. Next, we can use a NAND gate with one input connected to the output of the first NAND gate (Ā) and the other input connected to B. The output of this NAND gate will be ĀB.
b) Implementing AB:
To implement AB, we can simply use an OR gate with inputs A and B.
c) Combining ĀB and AB:
To combine ĀB and AB, we can use an OR gate with inputs connected to the outputs of the previous steps, ĀB and AB.
Therefore, the function f(A,B) = ĀB + (ABB) can be implemented using only NAND and OR gates.
Note: In the above steps, we assumed that you meant to use NAND and OR gates, as mentioned in the question. If you meant to use tS (Tie State) and z-input OR gates, please provide clarification, and we can adjust the implementation accordingly.
I hope this explanation is clear and helpful! Let me know if you have any further questions.