Digital logic gates are the building blocks of the digital circuit. Each basic logic gate implements a unique Boolean function and a complex Boolean expression is implemented using the network of basic gates. The three basic logic gates are:
- AND Gate.
- OR Gate.
- NOT Gate.
AND Gate implements the Boolean AND function, OR gate implements the Boolean OR function and likewise NOT Gate (also called Inverter) implements the Boolean NOT function. The Boolean expressions of each basic gate along with their schematics symbol are shown in the following figure.
The input and output variables of the Boolean function can assume any one of two possible values called ‘0’ or ‘1’. In terms of positive logic ‘0’ is considered to be low and ‘1’ is considered to be HIGH, whereas in terms of the negative logic ‘0’ is considered to be HIGH and ‘1’ is considered to be LOW. Any Boolean expression can be implemented using these three basic logic Gates.
Introduction to XOR Gate
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. 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 XOR Gate only.
XOR (Exclusive OR) Gate:
XOR Gate also referred to as Exclusive OR Gate is a digital logic Gate formed by combining three basic gates that is AND, OR and NOT Gates in a particular configuration. XOR Gate is a two input single output digital logic gate although it can also be configured for multi inputs. XOR 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 XOR Gate. The following image shows the schematic symbol and basic network configuration for the XOR Gate.
The XOR operation is represented by the ⊕ sign. Notice in the image that unlike NAND Gate and NOR the exclusive OR consist of the network to realize the XOR operation. The Boolean expression representing the XOR Gate functionality is as shown in the following figure:
Notice that the XOR functionality is represented by two Boolean expressions. Each Boolean expression is equivalent to the other and thus it implies that XOR 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 XOR Gate. Thus it concludes that multiple configurations can be employed to realize XOR Gate functionality. The Boolean Expressions along with their circuit implementation of XOR Gate are shown in the following image.
The equivalence of the two expressions can be verified using DeMorgan’s LAW. The Expression on the left is called product of sum and that on right is called sum of product.
XOR 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 XOR Gate along with its schematics symbol is shown below:
The output of the XOR (Exclusive OR) Gate is HIGH if and only if one of the inputs A and B of the XOR is HIGH otherwise the output will be LOW. Note that the output of the XOR Gate is HIGH when its inputs are different for same inputs the output is LOW thus the XOR Gate can be said to detect the equality of input variables.
Applications of XOR (Exclusive OR) Gate:
The Boolean function of XOR Gate is very important that makes XOR Gate very useful in digital systems. Although XOR Gate can be used in a variety of applications two most common and simplest applications of XOR Gate is its use in Half Adder and Full Adder. XOR Gate in combination to other basic can be wired to form Half Adder and Full Adder circuit. The circuits of Half Adder and Full Adder using XOR Gate are shown in the following image.
Half Adder and Full Adder perform the binary addition on binary inputs. The XOR Gate can also be used to design the comparator due to its unique truth table. In case of Half Adder the XOR solely can represent the sum two inputs binary variables the AND Gate is used to give the Carry bit. S represents the sum and C represents the Carry bit.
The equality comparator using XOR (Exclusive Gate) is shown in the following figure.
XOR Gate IC 7486
XOR gates are available in the IC packages. The TTL (Transistor-Transistor Logic) and CMOS (Complementary Metal Oxide Semiconductor) technology is used to designed XOR gate. One of the most popular IC for XOR Gate is 7486 which is a QUAD two inputs XOR Gate IC which means that this IC contains four independent two input XOR Gates. The pinout and connection diagram of the 7486 IC is shown below:
XOR GATE Symbol
That is all for now I hope this article would be useful for you. In the next article I will come up with more interesting topics. Till then stay connected, keep reading and enjoy learning.