Question

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

a) x ⊕ y
b) x ⋅ y
c) x' ⋅ y
d) x ⋅ y'

Answer 1

The XOR operator can be constructed using only NAND gates by following a step-by-step process.

Step-by-step explanation:

The XOR (Exclusive OR) operator can be constructed using only NAND gates. The XOR operation returns true if the inputs differ, and false if the inputs are the same. Here's the step-by-step process:

1. Start with the inputs x and y.
2. Use NAND gates to compute x' and y' (the negation of x and y).
3. Use NAND gates to compute (x' ⋅ y)' and (x ⋅ y')' (the negation of x' ⋅ y and x ⋅ y').
4. Finally, use another NAND gate to compute the XOR of (x' ⋅ y)' and (x ⋅ y')'.

The XOR gate constructed using NAND gates will have the same truth table as the XOR operator.