CODEWITHSUNDEEP
booleanlogic
Abdus Sattar Bhuiyan
Abdus Sattar Bhuiyan

Reputation: 3074

How to make XOR gate using OR gate?

I want to make XOR gate using OR gate.I have tried but I have to use additional NOT gate to make an XOR gate. Is it possible to make an XOR gate using only OR gate? If so how can I do this? please help. thanks in advance.

Upvotes: 4

Views: 4122

Answers (3)

DivineBerserker
DivineBerserker

Reputation: 11

Although you cannot make a XOR Gate only with OR Gates, something you can do is have the same inputs (A and B) that you had running through the OR Gate connect to a NAND Gate. The outputs of the OR Gate and the NAND Gate would then be connected through an AND Gate. There is a simpler way to create a XOR Gate using this method.

Upvotes: 1

Nemo
Nemo

Reputation: 71525

The AND and OR functions are "monotone". By definition, this means if you start with any setting of input bits, then change one of the input bits from zero to one, the output can either stay the same or change from zero to one; it can never change from one to zero. You can prove this from the truth tables.

A composition of monotone functions is a monotone function. This is also easy to prove.

XOR is not a monotone function. (Consider a two-input XOR where both inputs are one, then change one to zero.)

Therefore, it is impossible to do what you are asking.

Upvotes: 4

Ignacio Vazquez-Abrams
Ignacio Vazquez-Abrams

Reputation: 798546

There is no SoP or PoS equation that will allow you to perform XOR with only OR gates; a minimum of 3 (non-XOR/XNOR) gates is required, including at least one inversion.

Upvotes: 1

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