About the XAND..

 We have different kind of basic digital gates, such as NOT, AND, OR and the Universal gates. Besides those we knew about the XOR ( Exclusive-OR ) logic. But why are we not informed about XAND ( Exclusive-AND )..?

To know about XAND possibility, let us see about the genesis of XOR..

The idea behind XOR gate:

Consider we have two inputs and an output. The OR gives output logic '1' if at least one input is logic '1', and the truth table, as we know, looks like:

A	B	Y = A OR B
0	0	0
0	1	1
1	0	1
1	1	1

To recognize the case of only one input getting '1', we are "excluding" the case of both events getting '1', creating the Exclusive-OR (So, the XOR truth table output is '0' if both inputs are '1').

A	B	Y = A XOR B
0	0	0
0	1	1
1	0	1
1	1	0

What about the XAND then..?

If we adapt same explanation for the AND gate as well, we have to remove the case of getting A and B as '1' at the same time. In that case, we do not have any output..! We just get zero as for all inputs, which will look like:

A	B	Y = A XAND B
0	0	0
0	1	0
1	0	0
1	1	0

But wait..

Consider the definition of AND gate as this - "the output will be zero if at least one input is zero"..

Now, the procedure of obtaining the exclusive would be roughly:

1. The actual case - Output will be zero if either one or both are '0'
2. Now, exclude the case of both inputs being '0', and replace the actual output '0' with '1'
3. Form the resultant truth table.

Then the proposed table looks like this:

A	B	Y = A XAND B
0	0	1
0	1	0
1	0	0
1	1	1

Came across this table previously..? Of course, you're right. It's the truth table for the logic popularly referred to as XNOR..!

So, in that way, our journey of finding a new logic ended up in merging with XNOR..

Thanks for reading..

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