Implement 'AND' function with 'XOR' function.



#6

Hi, everybody!

I appreciate it if someone could tell me how to implement 'AND' function with 'XOR' function.

Best regards,

Tal
email: td@chem.ch.huji.ac.il


#7

I'm almost 100% sure you can't. The XOR function can't tell the difference between '1,1' and '0,0' at it's inputs. Inverting the inputs/output in whatever combination makes a new gate with an XOR or XNOR function.

You can of course make and AND function from the following:

A AND B = NOT(A) NOR NOT(B)

This is not as silly as it seems as in transistor logic a NOR gate can be smaller/faster than an AND gate (which is made from an NAND gate followed by an inverter).

Please feel free to correct me on any of the above if I have made an error.


#8

It can also be accomplished with an OR and two XORs.

	| = OR  ^ = XOR

x ^ y ^ (x | y)

The logical reason an OR is required is that an XOR is derived from two ANDs, two NOTs, and an OR (or a logical equivalent thereof):

	(x & !y) | (!x & y)
So, if an AND is desired, the OR must be factored out which, of course, requires an OR operation.
#9

Tal,
What are you up to now ???????????

Joe

#10

If you were to bu trying to build an AND function from XOR gates, then it is indeed possible.

Imagine an XOR gate with one input held in a logic 1 state. The gate then acts as an inverter. Similarly, if the input is held low it acts as a non-inverting buffer.

Using an additional 2 diodes, and a resistor allows you to "wire-AND" the outputs of two buffers, and then buffer the output.

Depending on the nature of the surrounding logic, you could even dispense with the XOR gates :-)


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