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Important points

i) Bubbled AND ≡ NOR

ii) Bubbled OR ≡ NAND

iii) XOR gate is an odd number of 1’ detector, 

i.e. if the number of 1’s is odd ⇒ output = high

And if the number of 1’s is even ⇒ output = low

iv) Performing XOR operation on A ‘n’ times,

v) Performing  XNOR operation on A ‘n’ times, 

vi) If the number of inputs (n) is odd, XOR ≡ XNOR and if the number of inputs (n) is even, 

vii) If one input of XOR is inverted, it becomes XNOR.

viii) AND – OR logic ≡ NAND logic.

This equivalence is widely used when we have to find the “minimum number of NAND gates” required to implement a circuit. But, before applying this logic, the first step will always be to convert the given expression in SOP  (Sum of Product) form. This will be illustrated later.

ix) OR – AND logic ≡NOR – NOR logic

Just like point (viii), this equivalence is also widely used when we have to find the “minimum number of NOR gates” required to implement a circuit. But, here also, the first step will be to convert the given expression in POS (Product of Sum) form. This will also be illustrated later.