Question

Write the boolean expression of X-OR gate. How many basic gates are required to build a X-OR gate using basic gates?​

Answer 1

Answer:

2-input EX-OR (Exclusive OR) Gate

For a 2-input Ex-OR gate, the output Q is true if EITHER input A or if input B is true, but NOT both giving the Boolean Expression of: ( Q = (A and NOT B) or (NOT A and B) ).

Answer 2

Answer:

Giving the Boolean expression of: Q = AB + AB

The truth table above shows that the output of an Exclusive-OR gate ONLY goes “HIGH” when both of its two input terminals are at “DIFFERENT” logic levels with respect to each other. If these two inputs, A and B are both at logic level “1” or both at logic level “0” the output is a “0” making the gate an “odd but not the even gate”. In other words, the output is “1” when there are an odd number of 1’s in the inputs.

This ability of the Exclusive-OR gate to compare two logic levels and produce an output value dependent upon the input condition is very useful in computational logic circuits as it gives us the following Boolean expression of:

Q = (A ⊕ B) = A.B + A.B

The logic function implemented by a 2-input Ex-OR is given as either: “A OR B but NOT both” will give an output at Q. In general, an Ex-OR gate will give an output value of logic “1” ONLY when there are an ODD number of 1’s on the inputs to the gate, if the two numbers are equal, the output is “0”.

Then an Ex-OR function with more than two inputs is called an “odd function” or modulo-2-sum (Mod-2-SUM), not an Ex-OR. This description can be expanded to apply to any number of individual inputs as shown below for a 3-input Ex-OR gate.

3-input Ex-OR Gate