Question

Construct the XOR operator using only NAND gates. Hint: x XOR y = ((x' y)' (x y')')'

a) NAND(NAND(x, NAND(x, y)), NAND(NAND(x, y), NAND(x, y)))
b) NAND(NAND(x, y), NAND(NAND(x, y), NAND(x, y)))
c) NAND(NAND(NAND(x, y), x), NAND(NAND(y, x), y))
d) NAND(NAND(x, x), NAND(y, y))

Answer 1

The correct XOR operator constructed using only NAND gates is option (b) NAND(NAND(x, y), NAND(NAND(x, y), NAND(x, y))).

Step-by-step explanation:

The XOR operator, x XOR y, can be expressed using NAND gates as ((x' y)' (x y')')'. The expression breaks down into three NAND operations: x' NAND y, x NAND y', and the final result of these two operations NANDed together.

The correct expression is NAND(NAND(x, y), NAND(NAND(x, y), NAND(x, y))). This arrangement of NAND gates correctly implements the XOR operation.

Understanding the construction of logical operators using NAND gates is foundational in digital logic design. NAND gates are universal, meaning that any logical operation can be built using only NAND gates. The provided expression follows the logic of the XOR operation, ensuring that the output is true only when the inputs are different.

In summary, the XOR operator constructed using only NAND gates is accurately represented by option (b). This expression captures the essence of XOR logic and is a valid implementation using universal NAND gates.