A NAND B = ¬(AΛB)

A XOR B = ¬AΛB + AΛ¬B

We have to make XOR equation has the form of NAND.

We will use De Morgan's Theorem: ¬AV¬B = ¬(AΛB)

¬AΛ¬B = ¬(AVB)

¬AΛB V AΛ¬B = ¬ (AV¬B) V ¬ (¬AVB)

= ¬¬ ( ¬ (AV¬B) V ¬ (¬AVB) )

= ¬ ( (AV¬B) Λ (¬AVB) )

= ¬ ( (AΛB) V (¬AΛ¬Β) )

= ¬(AΛB) Λ ¬(¬AΛ¬Β)

= ¬(AΛB) Λ (AVΒ)

= (¬(AΛB)ΛΑ) V (¬(AΛB)ΛB)

= ¬¬((¬(AΛB)ΛΑ) V (¬(AΛB)ΛB))

= ¬( ¬ ( ¬(AΛB) Λ Α ) Λ ¬( ¬(AΛB) Λ B ) )

Now we have a NAND "¬(AΛB)" connected to a NAND with A as second

input, connected to a NAND that has one input from the first NAND and B, and both are connected to a NAND.

Note: V = OR, ¬ = NOT, Λ = AND

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