These basic digital logic gates that is AND, OR and NOT gates can be combined together in particular topologies to realize other important gates. The most common examples are NAND and NOR Gate.
Introduction to XNOR Gate
NOR Gate is formed by the combination of OR and NOT Gate in series that is by connecting the output of the OR at the input of the NOT Gate similarly NAND Gate is formed by the combination of AND and NOT Gate. Other important Gates formed by the combination of basic logic gates are XOR (Exclusive OR) and XNOR (Exclusive NOR) Gates. XOR and XNOR are formed by connecting AND, NOT and OR in particular configuration; we will see later that XOR or XNOR Gate can be formed in a variety of ways. Here the discussion in oriented to XNOR Gate only.
XNOR (Exclusive OR) Gate:
XNOR Gate also referred to as Exclusive NOR Gate is a digital logic Gate formed by combining three basic gates that is AND, OR and NOT Gates in a particular configuration. XNOR Gate is a two input single output digital logic gate although it can also be configured for multi inputs. XNOR Gate operates on the inputs in such a way that the network of AND, OR and NOT processes the inputs and generates the output according to the Boolean expression representing the XNOR Gate. The following image shows the schematic symbol and basic network configuration for the XNOR Gate.
The XNOR operation is represented by the sign. Notice in the image that unlike NAND Gate and NOR the exclusive NOR Gate consist of the comparatively complex network to realize the XNOR operation. The Boolean expression representing the XNOR Gate functionality is as shown in the following figure:
Notice that the XNOR functionality can be represented by two Boolean expressions. Other Boolean expression can be derived by using the De Morgan’s Theorem. Each Boolean expression is equivalent to the other and thus it implies that XNOR Gate can be implemented by multiple configurations. Recall from the discussion on NAND Gate and NOR Gate that being universal Gates they can also be used to implement the Boolean expression of XNOR Gate. Thus it concludes that multiple configurations can be employed to realize XNOR Gate functionality. The Boolean Expressions along with their circuit implementation of XNOR Gate are shown in the following image.
The Boolean expression on the left is called the product of sum and other expression derived from the DeMorgan’s Theorem is called as Sum of product.
XNOR GATE Truth Table:
The relation between the state of the output variable and that of the input variables is represented in the form of the table. This table is called the Truth Table. The Truth Table of the XNOR Gate along with its schematics symbol is shown below:
The output of the XNOR (Exclusive OR) Gate is HIGH if and only if both of the inputs A and B of the XNOR are HIGH otherwise the output will be LOW. Note that the output of the XNOR Gate is HIGH when its inputs are same, for different inputs the output is LOW thus the XNOR Gate can be said to detect the equality of input variables. Also note from the truth table that the output of the XNOR Gate is the exact complement of the XOR Gate.
Applications of XNOR (Exclusive NOR) Gate:
The Boolean function of XNOR Gate is very important that makes XNOR Gate very useful in digital systems. Although XNOR Gate can be used in a variety of applications one of the most common and simplest applications of XNOR Gate is its use in Full Adder circuit. XNOR Gate in combination to other basic gates can be wired to form Full Adder circuit. The circuit of Full Adder using XNOR Gate is as shown in the following image.
Full Adder performs the binary addition on binary inputs. As shown in the circuit above the full adder has three inputs A, B and CarryIN and two outputs SUM and CarryOUT. The XNOR Gate can also be used to design the comparator due to its unique truth table. The equality comparator using XNOR (Exclusive Gate) is shown in the following figure.
XNOR Gate IC 74HC266N
XNOR gates are available in the IC packages. The TTL (Transistor-Transistor Logic) and CMOS (Complementary Metal Oxide Semiconductor) technology is used to designed XNOR gate. One of the most popular IC for XNOR Gate is 74HC266N which is a QUAD two inputs XNOR Gate IC which means that this IC contains four independent two input XNOR Gates. The pinout and connection diagram of the 74HC266N IC is shown below:
XNOR Gate SYMBOL
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