What is the minimum number of NAND gates required to implement the Boolean function f = x'y + xy' is

Correct option is B

To implement the Boolean function f = x'y + xy' using NAND gates, first need to simplify the given function and then break it down into NAND gate equivalents.
Step-by-step Implementation:
The given function is:
f = x'y + xy'
This is an XOR function (Exclusive OR), which can be implemented using NAND gates. The XOR operation can be represented as:
f = (x NAND (x NAND y)) NAND (y NAND (x NAND y))
Now, calculate the number of NAND gates required:
1. x NAND y: 1 NAND gate.
2. x NAND (x NAND y): 1 more NAND gate.
3. y NAND (x NAND y): 1 more NAND gate.
4. (x NAND (x NAND y)) NAND (y NAND (x NAND y)): 1 more NAND gate to complete the XOR function.
Thus, a total of 4 NAND gates are needed.
Important Key Points:
1. XOR Function: The function x'y + xy' is essentially the XOR operation, which can be implemented using NAND gates.
2. NAND Gate Implementation: The XOR function can be implemented using 4 NAND gates.
3. Gate Count: The minimum number of gates required to implement this Boolean function is 4.
Knowledge Booster:
· NAND Gate Properties: NAND gates are versatile and can be used to implement other gates such as AND, OR, and NOT. For an XOR function, multiple NAND gates are required to form the necessary connections.
· AND, OR, NOT Gates: While these gates are fundamental in Boolean algebra, they need additional gates (like NAND gates) to be implemented more efficiently in digital circuits.