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To create an XOR gate using only NAND gates, you can follow a specific sequence of operations. The XOR gate outputs 1 when the number of high inputs is odd, and 0 otherwise. Here's how you can achieve this using NAND gates:
Example
def nand(a, b):return not (a and b)def xor(a, b):# Step 1: A' = NAND(A, A)a_nand_a = nand(a, a)# Step 2: B' = NAND(B, B)b_nand_b = nand(b, b)# Step 3: A'B = NAND(A', B)a_nand_a_and_b = nand(a_nand_a, b)# Step 4: AB' = NAND(A, B')a_and_b_nand_b = nand(a, b_nand_b)# Step 5: XOR = NAND(A'B, AB')result = nand(a_nand_a_and_b, a_and_b_nand_b)return result# Test the XOR functionprint(xor(0, 0)) # Output: False (0)print(xor(0, 1)) # Output: True (1)print(xor(1, 0)) # Output: True (1)print(xor(1, 1)) # Output: False (0)Explanation
Step 1: Compute A' using NAND(A, A).
Step 2: Compute B' using NAND(B, B).
Step 3: Compute A'B using NAND(A', B).
Step 4: Compute AB' using NAND(A, B').
Step 5: Finally, compute the XOR result using NAND(A'B, AB').
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