until now we have seen the three basic Gates which are the and gate or gate and the not gate so these are the basic Gates let us look into some more some more gates like the xor gate and the xor gate let's start with the xor gate the true table for the xor gate is as follows it has two inputs and one output if you have two inputs you have four combinations so as per the exor gate if both the inputs are same then the output is a zero so here in this case A and B are equal so the output is zero and in this case again A and B are one so the output is zero and when both the inputs are different then your output is a one so this is the XR gate now to come up with the Boolean expression for f or for the xor gate we take the situation where f is one so that's this case and this case so when f is one let's go for this case a is a zero so we write a prime and B is a one or when we go for the second case a is one so we write a and B is zero B Prime so this is the expression for an xor gate a prime B plus a prime this can also be written as f equals a XR B so this is the symbol for the XR gate the gate symbol for the XR gate is as follows it has two inputs A and B and it has one output so it's the orgate and with an extra curved line at the beginning of the orgate your X orgate is also known as the exclusive orgate it is used in parity Checkers let's go for the xgate the true table for the xor gate is as follows as the name suggests it is the inverse of the XR gate so you have two inputs and one output with four combinations of inputs now as per the xor gate when both the inputs are same the output is a one and if both the inputs are not same the output is a zero your xor gate is also known as the equivalence gate because because when both the inputs are same the output is the output is one the equation for the X gate would be f equals we consider this case and this case so f is one when both A and B are inverted or F is one when both A and B's are ones therefore f equals this is the symbol for the xgate so that completes XR and xnor gate let's look at some properties for the XR gate the first property is what is a xr0 let's take the equation again a XR b equals a prime b + a prime in this case b is a zero so you have a prime 0+ a 0 Prime is 1 so that's a so a X or Z is equals to A let's go for the next one which is what is a X or 1 take the formula again a prime b + a prime so a prime B is a one or a b Prime since B is a one b b Prime will be zero so this would be a prime there are some of properties like a X or b equals b x or a they are one and the same and you have a X or B X or C equals ax or BX or c