XNOR EXPRESSION SERIAL

The Ex-NOR gate outputs logic вЂњLOWвЂќ when inputs have different logic states.The output of the Ex-NOR logic is вЂњHIGHвЂќ when both of the inputs have the вЂњSAMEвЂќ logic states.Figure 7: A Multisim circuit showing XNOR logic to control an external circuit Conclusion When inputs are at different levels, XNOR logic goes вЂњOFFвЂќ turning the relay and lamp to вЂњOFFвЂќ state. The relay thus turns on the lamp through an external circuit of 12V. The XNOR gate turns on the relay when all of the inputs are connected to VCC/ Ground. In the following figure, an XNOR gate is used to drive a 12V relay to switch on the lamp using NI Multisim. The most commonly used XNOR logic packages are: CMOS based XNOR Gate IC PackageДЇigure 6: 74LS266 & CD4077 XNOR Quad Package The XNOR logic gates are available in both TTL and CMOS logic families. Commercially Available E-NOR (XNOR) Gates They are also used in data error detection circuits as Parity Bit Checkers. The Exclusive-NOR logic gates are helpful in performing arithmetic operations and computations. The construction of the Ex-NOR gate using NAND gates only is shown below: Figure 5: Equivalent Circuit of an Exclusive-NOR logic using NAND Gates However, it is not a good practice to include multiple logics for the construction of logic gates and a better Ex-NOR circuit can be constructed using only NAND logic gates. The above equivalent Ex-NOR logic comprises AND, OR, and NOT logic. Figure 4: Equivalent Circuit of an Exclusive-NOR logic Using the logic expression of a two-input Ex-NOR logic, an equivalent circuit can be constructed which is shown in the following figure. The symbol and expression of a 3-input Ex-NOR logic are given below: Figure 3: Three input Ex-NOR Gate Symbol with expression Ex-NOR (XNOR) Logic Circuit This characteristic makes the Ex-NOR an even gate. The Ex-NOR logic gives a вЂњHIGHвЂќ output when inputs with the logic вЂњHIGHвЂќ are in even numbers except for the case when all of the inputs are вЂњOFFвЂќ or at logic вЂњLOWвЂќ. Whereas, the Ex-NOR logic is an even function which is eminent from the truth tables given above. The truth table of a three-input Ex-NOR logic is as follow and can be expanded to include any number of inputs:ДЄs discussed in the previous article, the Ex-OR logic is an odd function and gives a logic вЂњHIGHвЂќ output when there is an odd number of inputs having logic вЂњHIGHвЂќ or вЂњ1вЂќ. In other words, the expression is вЂњAвЂќ AND вЂњBвЂќ, Same! either вЂњ00вЂќ or вЂњ11вЂќ state then the Ex-NOR logic output is вЂњHIGHвЂќ and in case the inputs are at the different levels then output is вЂњLOWвЂќ. It is clear from the truth table that when inputs are at the same levels i.e. The truth table of a two-input Ex-NOR logic is shown below: The symbol of the Ex-NOR logic is similar to the Ex-OR logic except for an вЂњInversion BubbleвЂќ which is added at the output to denote the вЂњNOTвЂќ function. The representation of an Ex-NOR logic by a symbol is shown in the following figure. The equivalent circuit of an Exclusive-NOR gate is: Figure 1: Exclusive NOR logic equivalent Logic Ex-NOR Gate Symbol & Truth Tables The Boolean algebraic equation of an Ex-NOR logic is given below: However, the Ex-NOR gateвЂ™s output goes вЂњHIGHвЂќ again when both of its inputs go to logic level вЂњHIGHвЂќ. The truth table of the logic NOR gate is somewhat similar to the Ex-NOR gate in that its output remains at logic level вЂњHIGHвЂќ and goes to вЂњLOWвЂќ when any of its inputs goes вЂњHIGHвЂќ. Because of its construction from multiple basic logic gates, it is also called a вЂњhybridвЂќ logic gate. Similarly, the Ex-NOR gate is also commercially available as a separate logic gate. Similar to the Ex-OR gate, the construction of Ex-NOR logic is complex compared to other logic gates and is constructed using basic logic gates. The Ex-NOR is a very useful logic and is mostly used in circuits involving arithmetic operations such as Parity Checkers, Adders and Subtractors, etc. The Exclusive-NOR is also referred to by writing only Ex-NOR or XNOR. The Exclusive-NOR gate outputs logic вЂњHIGHвЂќ only when both of its inputs are equal and, therefore, it is sometimes referred to as вЂњEquivalence GateвЂќ. In the case of, either вЂњAвЂќ or вЂњBвЂќ that is вЂњ01вЂќ or вЂњ10вЂќ the output of the Exclusive-NOR gate will be вЂњLOWвЂќ. It means that the output of the Exclusive-NOR gate is вЂњHIGHвЂќ when both inputs вЂњAвЂќ and вЂњBвЂќ are at the same logic level i.e. The Exclusive-NOR gate gives an output given by the expression вЂњBoth A & B, not A or BвЂќ.

XNOR EXPRESSION SERIAL

It is the serial combination of Exclusive-OR and the NOT gates. The Exclusive-NOR logic is the complement (reverse) form of the Exclusive-OR logic.

Xnor expression