3-Input Ex-OR Gate Logic Symbolįor 3-input XOR gates, we can have the HIGH input when odd numbers of inputs are at HIGH level. The truth table and logic symbol for 3-input XOR gate is given below. Q = A ⊕ B ⊕ C = A B C + A B C + A B C + A B C The Boolean function for the 3- input XOR gate is: More than 2 input XOR function is called as “Odd function” or “Modulo-2 sum”. In some cases, we need to have XOR Gates with more than 2 inputs. The pulsed operation of 2 input XOR gate is shown below. The first term in the above equation requires an OR Gate, the second term needs a NAND gate and the final equation can be obtained using an AND gate. For this, we have to re-write the above XOR Boolean Equation. Let us now see how we can implement the XOR Gate using NAND, AND and OR Gates. The following image shows the XOR Gate implemented using NAND Gates. This equation looks like it can be implemented using NAND Gates. Q = (A ( A B ))’ (B ( A B ))’ = (A (AB)’) (B (AB)’)įinally, once again, apply complement on both sides. Q = A ( A B ) + B ( A B ) = A (AB)’ + B (AB)’ Now we need to implement this circuit using NAND gates. Q = (A + B) ( A + B ) = (A + B) (A’ + B’)Īpplying de Morgan’s Law on the second term in the above equation, we get:
Let us now see how we can implement the XOR Gate using NAND Gates. The following image shows the XOR Gate implemented using NOR Gates. We need totally five NOR gates (two for inverting A and B, one for NOR of A and B, one for NOR of A’ and B’ and the final one to obtain the above equation). This equation looks like it can be implemented using NOR Gates. Once again taking complement on both sides, we get: Let us now see how we can implement the XOR Gate using NOR Gates. An EX-OR gate can be designed by using basic logic gates like NAND gate and NOR gate as they are universal gates. If a specific gate is not available directly, we can design the XOR Gate by using multiple gates. If both the inputs are same, then the output is LOW. The output of 2 input XOR gate is HIGH only when one of its inputs are HIGH. So, the XOR circuit with 2 inputs is designed using AND, OR and NOT gates as shown below. From the above calculations, the main Boolean Expression of XOR gate is: The EX-OR gate is defined as a hybrid logic gate with 2 inputs to perform the Exclusive Disjunction operation. (A + B) (A B) XOR Gate Equivalent Circuit If A and B are the inputs of the XOR gate, its output is given as:īy applying De Morgan’s law, the above Boolean expression can also be written as: Using the above truth table and corresponding K-Map, we can now derive the Boolean Expression for XOR Gate. The K-map representation of the above truth table of the XOR Gate is shown below. Low logic that is logic ‘0’, at its output, when When the two inputs are different it produces a logic high value i.e., logic ‘1’ at its output.
From this, it is clear that XOR gate produces a logic LOW i.e., Logic ‘0’ at its output, when both the inputs are same (both may be LOW or both may be HIGH). The truth table of XOR gate is shown in the below table.
We have to use the Karnaugh Maps or K – Maps along with the truth table to derive the Boolean Expression of XOR gate. As it is a Hybrid gate, the Boolean expression of output of XOR gate is given by a combining of Multiplication, Addition and inverting of inputs. The Boolean expression for XOR gate cannot determined directly like AND, OR gates. The XOR logic symbol in IEEE and IEC standards is shown below. Generally, we follow the IEEE (Institute of Electrical and Electronics Engineers) and IEC (International Electrotechnical Commission) standards. There are multiple standards for defining an electronic component. If both the inputs are LOW or HIGH, then the output is LOW. Commonly Available TTL and CMOS Logic Ex-OR gate IC’sĮxclusive OR Gate, also known as EX OR Gate or XOR Gate, is an important digital logic gate, which implements an exclusive or logic i.e., the output is HIGH if and only if one of the inputs is HIGH.