Question

Implement the function below with a decoder and external logic gates.
F=(x⊕yz′)′+x′y

Answer 1

The question asks for implementing a Boolean function using a decoder and external logic gates. It involves generating minterms with a decoder and combining them using logic gates. NOT gates are also used for input complementation where necessary.

Step-by-step explanation:

The question involves implementing a Boolean function F with a decoder and external logic gates. The function given is F=(x⊕yz′)′+x′y, where ⊕ is the XOR operation, ′ is the NOT operation, and + is the OR operation. To implement this using a decoder and logic gates, you would need to do the following steps:

• Identify the minterms of the function.
• Use a decoder to generate the minterms.
• Combine the minterms using OR gates to get the final function.

For the given function:

1. Decompose the function into minterms.
2. Use a decoder to generate the required minterms based on the inputs x, y, and z.
3. Select the relevant minterms and connect them through an OR gate.
4. Add any necessary NOT gates to complement inputs as required (for x′ and z′).
5. Finally, connect the outputs from the OR gate and the AND gate (for x′y) to another OR gate to get the function F.

Remember to use NOT gates where needed to create x′ and z′ before feeding them into the decoder or the AND gate. By using a combination of a decoder and logic gates like AND, OR, and NOT, you can construct the desired logical function F.