No. OR is not functionally complete, so you can not use it to derive any other logical expression. The reason for this is because you can only construct the following expressions out of only OR gates:
A OR B
A OR A
Because of the Idempotency theorem, A OR A simply reduces to A, so we are left with A OR B, which we can not use to derive any other logical circuits. At the very least, we would also need a NOT gate.
This is why NOR and NAND are functionally complete: you can derive a NOT gate by using A NAND A or A NOR A.
xor and xnor gates are derived from not gate
Its possible to design a 4-i/p xor gate using only 2-i/p nand gates Although the design turns out to be quite complex and comprises of 21 NAND gates : F = (A'B+AB')(C'D'+CD) + (A'B'+AB)(C'D+CD') Above given equation is the o/p equation for the circuit .
yes... xor is derived gate from primary gates
No, XOR gate is a not a universal gate. There are basically two universal gates NAND and NOR.
To make a full subtractor, you need an XOR and a NAND gate.
Three 2-input XOR gates and one 3-input NOR gate will do the work. Connect each output of each XOR gate to one input of the 3-input NOR gate and apply the two 3-bit words to the inputs of the XOR gates. If X (X2X1X0) and Y(Y2Y1Y0) are two 3-bit words, X2 and Y2 will connect to one XOR gate, X1 and Y1 to the next XOR gate and X0 and Y0 to the last XOR gate. You could see the result of the operation on a LED connected to the output of the NOR gate. Other implementations are also possible of course. The solution above is absolutely correct, but includes a 3 input gate. If the task is to use only two input gates, then a small change will be needed. Take the outputs from any two XOR gates into a 2 input OR gate. Then take the output of the OR gate and the output of the third XOR gate into a 2 input NOR gate. The operation remains identical to the first solution but adheres to the brief of using gates with 2 inputs. In the real world, there is probably no reason to impose such a limitation on a design so the first solution would normally be the preferred route to take.
its not
a XOR bis equivalent to: (a AND NOT b) OR (b AND NOT a)
XOR (Exclusive OR) gate is exclusively for either. OR allows 10, 01, 11. XOR allows 10 or 01, but not 11.
XOR (Exclusive OR) gate is exclusively for either. OR allows 10, 01, 11. XOR allows 10 or 01, but not 11.
1 gate.
As such an OR gate should do the job...but if the question is of using gates other than the simple OR, it should be a combo of NOR and NOT gates; where-in, the NOT gate comes after the NOR gate. Factfully speaking: The output of a NOR gate when fed to a NOT gate shall give you an OR gate. cheers :) Anish Murthy Airpula, RF Design Engineer (F.A.E) Ceramic & Microwave Products Group, Dover Corporation Inc, United States of America