Digital Logic Design Principles - Research Paper Example

TABLE OF CONTENTS: Contents TABLE OF CONTENTS: 1 List of Figures TABLE OF CONTENTS: 1 Introduction Since antiquity logic has been used to abstract arguments in the ordinary language. George Boole introduced the first serious mathematical representation in the mid-1800s. Later on, the concepts of Boolean algebra would be developed further by Claude Shannon in 1937 where he used the algebra in switching to electronic switching circuits. By 1950s, Boolean principle had already become a standard part of the electronic design. Towards 1970s, there was the development of programmable Logic Arrays (PLAs) that were specifically used in the application of Specific Integrated Circuits (ASICs) (Nicolas and Joachim, 89). Mechanical and diagrammatic methods can be traced back to the medieval times. Since their development, there later came more systematic methods that would assist in reducing complexity in expressions. Karnaugh map was introduced in the 1980s and were developed further to computer programs that promoted Boolean minimization to the large scale. Today, a number of Boolean minimization types have been used in circuit and chip design since 1990s. What are Logic Gates? Logic gates have been defined as elementary building blocks that take in one or more electronic signals from a circuit, and sends an output signal based on that output. The common logic gates come with two inputs and one output. At any point in time, all terminals will be in one of two binary conditions including the high (1) or low (0) and this will be marked by different voltage levels. In a common logic gate the low state generally has zero volts (0 V) and the high state generally has five volts (+5 V). The logic gates are placed in a way that enable them determine how data is physically processed in a computer (Nicolas and Joachim, 91). An example of a device emitting logic signals would a telephone that converts the speaker’s voice signal to a sequence of zeros and one. The zeros and ones will then be interpreted by the device of the receiver and then converted back to a language that can be understood by the Requirements of Logic Gates Power Supply: Logic gates will need power to function. Here the designer/user will pick a voltage signal which he will use as working example. The mostly taken values are low level (represented by 0V) and high level (represented by 1V) (Nicolas and Joachim, 95). The signals will usually change as time changes and this makes the system dynamic. This is why the operation of logic gates calls for understanding of how diodes and transistors work. INPUTS: The gate inputs will be driven by voltages. To recognize this for example, 0V and 5V will be used to represent logic 0 and logic 1 respectively. The higher the voltage level, the more the driving power of the input will be, depending on the type of electric control being used. The inputs are crucially important as they determine the value of the output. OUTPUTS: The major characteristic used to represent the output of a logic gate is that it comes with two voltage nominal values. For example 0V and 5V may be used to represent logic 0 and logic 1 respectively. The common logic gates will have only one output but there are others with more than one output. Normally, a variable will always be associated with a logic signal and a symbol in this case can be assigned to represent the variable. Logic Gates Types and Truth Tables There are basically seven types of logic gates including; NAND, AND, OR, XOR, NOT, NOR, and XNOR. To show the function of a logic gate however, one will need to use Truth tables. Truth tables are specially designed tables to help understand the behavior of logic gates (Norman, and Carlson, 108). The truth tables will shows how the input of the logic gate relates to the output. The gate columns will be shown in the left columns of the table with the various combinations of input. The gate outputs are shown on the right hand. Figure 1: Truth table AND Gate The distinctive characteristic of the AND gate is that it will only give a high output if, and only if the inputs are high. The gate derives its name from the argument that it will act in the same way as the typical logic “and” operator as long as the 0 is called “false” and 1 is called “true” (Norman, and Carlson, 110). Below is a diagram representing an AND gate and a corresponding Truth table, meant to interpret the gate. Figure 2: AND Gate The above diagram shows the circuit symbol and the logic combination of for an AND gate. As we can see here above, the output terminal is at the right and the input terminal at the left. The output will be “true” when both inputs are “true”. If this condition is not met, the output will be “false” (Norman, and Carlson, 113). The operation of the AND logic is shown by the use of a dot (.) i.e. A.B. In some instances, the dot may be eliminated to make it AB. OR Gate The OR gate is an electronic circuit known to give a high output (1) as long as one or more of the inputs are high. Here, the plus (+) sign represents OR operation. Figure 3: OR Gate The OR derives its name from the observation that it works out after the fashion of the logic inclusive “or”. What this interprets to is that the output will be “true” if either or both of the outputs are “true”. Contrary to the case of AND gate, only one of the inputs will be required to true for the output to be “true” (Norman, and Carlson, 115). However, if it turns out that both the inputs are “false” the output will end up becoming “false” just like in the case of AND input. NOT Gate The NOT gate is a form of electronic circuit that gives out an inverted version of the input at the output terminal. For this reason, the NOT gate is also referred to as the inverter. If the input at the terminal is for example A, the output at the output terminal will be the inverse of A, or simply put, “NOT A”. Below is a diagram showing a NOT gate and its Truth table. Figure 4: NOT Gate As it can be seen here above the input ‘A’ produces an output with a bar on top (A-bar). In the diagram also, it is clear that the NAND logic gate can be configured in two ways to come up with a NOT gate (Norman, and Carlson, 118). The NOT gate can also be produced with the use of NOR logic gate using the very same concept as shown here below. NAND Gate The combination of NOT and AND gate forms the NAND gate. As such, the NAND gate will be equal to an AND gate with the NOT gate coming after it. Using the same principle in the NOT and AND gate, it is clear that the outputs of all NAND gates will be high as long as any of the outputs is low. The symbol of a NAND gate is generated by taking the symbol of the AND gate and adding a small circle on the output (Claude and House, 36). The small circle added on the output in the AND gate will in this case represent inversion. Below is a diagram showing a NAND gate with a corresponding truth table. Figure 5: NAND Gate In the diagram above it is clear that the NAND gate acts in a way of the logic operation “and” which is immediately followed by negation. This brings forward the conclusion that the output will be “false” if both inputs are “true.” Otherwise, the output will come out to be “true.” NOR Gate The NOR gate is also referred to as the NOT-OR gate. It is formed from the combination of the NOT and OR gate. What this means is that it will be equal to an OR gate followed by a NOT gate. The diagram below shows a NOR gate with a corresponding truth table. Figure 6: NOR Gate The output of the NOR gate will be low if any of the inputs are high. The symbol of an OR gate is derived from taking the OR gate and adding a small circle on the output. The added small circle in this case represents an inversion. From the above diagram, it is also clear that the output will be “true” if both inputs are “false.” Otherwise, the output will be “false.” EXOR Gate The EXOR gate is also known as the Exclusive-OR gate. This is a form of a circuit that will tend to give a high output if neither, but not both, of the inputs are high. The EOR operation in this case is shown with an encircled plus sign () (Claude and House, 38). The diagrammatical representation of the EXOR gate and the Truth table is shown here below. Figure 7: EXOR Gate The EXOR gate operates the same way as the logic “either/or.” What this means is that the output will be true if either, but not both, of the inputs are “true.” Also, the outputs will be “false” if both inputs are “true” or if both inputs are “false”. The output will thus tend to be 1 if there are different outputs and 0 if there are same outputs. EXNOR Gate The EXNOR gate is also known as exclusive-NOR gate. It is a form of circuit that does the exact opposite of the EOR gate. In such a case, it will give a low output if either, but not both, of its inputs are high. It symbol can be derived by taking the EXOR gate and adding a small circle on the output. The diagram below shows an EXNOR gate with a Truth table. Figure 8: EXNOR Gate The XNOR gate can be developed from the use of a combination of XOR gate followed by an inverter. What this interprets to is that the output will be “false” if the inputs are not the same and “true” if the inputs are the same. Logic gate designers have used combinations of logic gates in coming up with complex operations that suit various business operations. Theoretically, there is no given number of gates that can be applied in a single device. However, this is not the case in practice as there is a given limit on the number of gates that can be installed to a given physical space. Integrated Circuits (ICs) are good examples of logic gates (Claude and House, 41). Engineers have discovered that the physical volume of a given gate has continued to decrease as more progresses are made in the development of IC technology. What this interprets to is that in the future, digital tools of same or smaller sizes will be able to take on much bigger tasks with an increased speed and efficiency. Improve logic gates also enable the carrying out of complex mathematical functions. Combined Logic Gates Representation using the Truth Table For simplicity in understanding the operation of the gates, designers have combined all the gates by representing them in the Truth table. As earlier stated, a Truth table is basically tables to help understand the behavior of logic gates. Using the combined Truth table is important in determine where to use which gate in attaining the best decision. The combined logic gates are shown in the Truth table here below. Figure 9: Combined logic Gates representation Universal Logic Gates The concept of Universal was first mentioned by Charles Sander’s Peirce in the 1880 who noted that NAND gates alone or NOR agates alone could be used to reproduce the functions of all the other logic gates. From this point, the uniqueness of both NAND and NOR gates could not go unrecorded. It however took long before this concept could be fully adopted in 1930. From this point, the NOR logic operation was named as Peirce’s arrow and NAND was also referred to as the sheffer stroke (Claude and House, 46). Also from this moment, both the NAND and NOR logic gates have been referred to as the universal logic gates. Figure 10: Universal logic gates Three-State Logic Gates A three-state logic gate is basically a type of logic gate with three different outputs. Typically, the common logic gate has one output. However there has been the development of logic gates with more than one output say two or three outputs. A tri-state logic gate has three outputs including; low (L), high (H), and high-impedance (Z) (Claude and House, 57). The high-impedance state in this case plays no role and this means that it is strictly binary. The devices are mainly used in buses of a CPU with the work of allowing data to be sent over multiple chips. Using three-state logic gates to drive a line is critically important as it provides a more stable control circuit that in such a case can be equated to a multiplexer. The use of the three-state multiplexer also allows the physical distribution of plug-ins in cards and other separate devices. In the field of electronics, a relatively low output would imply that the output is getting current from the terminal with zero voltage (-ve power) (Claude and House, 62). On the other hand, a relatively high output would imply that the output is getting current from the terminal with positive voltage (positive power). In such a case, the presence of high impedance would imply that the output is not in any way connected to the circuit. Figure 11: Three-state logic gates The diagram above shows a typical tri-state logic gate. This type of a tri-state logic gate can also be perceived to be a switch. The switch will be open when B is turned off. Also, the switch will be closed when the B is turned on. There is more than one output in this case. De Morgan Equivalent Symbols De Morgan has come up with a law that proves that the OR and AND function are identical with negated inputs and outputs. The same way, the OR state functions with negative inputs will be equivalent to a NOR gate to an AND gate with inputs that are negative. With this kind of argument, there has been the development of alternative symbols the common gates with the capability to use the core symbol including OR or AND where outputs and inputs have been negated (Claude and House, 78). The use of alternative logic symbols is important because it simplifies the use of circuit diagrams and makes them clearer. With that, they will be able to point out areas that are accidentally connected of an active low input to a higher input. Areas that are found having negations on both ends will be replaced with connections that do not have negations. A path will be said to have no logic negation if it is ascertained that there is a match of polarity indicators on both ends (Claude and House, 81). It will thus be wrong to constantly associate AND with OR shapes without taking into consideration the bubbles that may come up at both the output and input terminals when estimating the “true” value of the expressed logic function. Figure 12: Equivalent symbols in logic gates Applications of Logic Gates Since their full developments in early1990s, logic gates have been applied in CMOS technology. Here, logic gates have been used to make PMOS and NMOS transistors that are later used to make common electronic devices (Mohamed, 92). Most of the digital devices where logic gates are used are meant to perform many functions that are complicated and tedious. As such, millions of logic gates need to be packed together to help execute multiple complex functions. The common digital devices will today not run without logic gates that serve many proposes including; control of voltage from one point to another, encoding transmitted information, and switching on or off as needed by the user. A number of logic families come with different unique characteristics pertaining to size, cost, speed, and power consumption. What this means is that the logic gate families can be used in the optimization of the speed of executions. All a user has to do is to select a logic gate family that fits his/her situation. The fast execution of tasks by comes as a solution to PMOS transistors that are said to be relatively slower than the logic gates. The various logic families include; Complementary Metal Oxide Semiconductor (CMOS), Transistor-Transistor Logic (TTL), Diode Transistor Logic (DTL) Resistor-Transistor Logic (RTL), and Resistor-diode Logic (RDL) (Mohamed, 99). All these logic gate families have helped optimize how people communicate with each other as well as how companies do business and share information. Before the introduction of MS Dos and Windows, engineers actually relied upon logic gates made out of DNA to create computers. In fact, it has been put to record that a computer going with the name, MAYA, was made from logic units created out of DNA, more specifically, DNA nanotechnology. The developments on the logic gates have contributed greatly to the increased technologic developments and innovation of digital devices. What makes Logic Gates? Electromagnetic Relays: Electromagnetic relays are known to be good at making logic gates. A really is basically a switch that need electric operation. The relay operates a switch through the use of mechanical electromagnets and other principles such as solid-state relays. In the logic gate relays will be used to control a circuit with the use of low-power signals. The very first relays were used in the making of a logic gate that controlled distant telegraph circuits. They were also used in early computers in the performance of logic operations. Logic gates made out of DNA. Logic gates have also been made out of DNA through DNA nanotechnology. In this process, there will be the manufacture of artificial nucleic structure to be used in the non-biological engineering materials. Engineers have been able to manufacture logic gates out of DNA owing to the structures’ tetrahedron nature (Mohamed, 103). Tetrahedrons in this case work as multiple switches rendering the functionality needed in the making of a logic gate. The DNA tetrahedron nature is represented in the diagram below. Figure 13: Tetrahedron DNA used to make logic gates Logic gates made from Quantum Mechanical Effects: Engineers have also been able to make logic gates from quantum mechanical effects through a process known as quantum computing (Mohamed, 116). In quantum computing, logics such as entanglement and superposition have been used to perform multiple operations on data. Quantum computing makes use of bits (qubits) in the sharing of theoretical similarities with probabilistic and non-deterministic computers. The concept of quantum of quantum computing was first mentioned in the 1980s by Yuri Manin (Mohamed, 111). When used in a logic gate, the quantum computer spins as quantum bits, providing a switch component that opens and closes operations just like today’s normal commands in Windows. Figure 14: Block sphere representing a qubit, Conclusion It is in no doubt that we conclude that logic gates are important building blocks to digital logic circuits with the application of combinational logic. Logic gates are called “gates” because they logically the control of information. It is therefore important to understand the operation of logic units in order to know how various synthetic regulatory networks are meant to work. Additional research and development on logical gates is required so that people can make in new opportunities and efficiencies attributed to the gates. As the internet revolutionizes individual and business activities there is need to match it with the logic gates. Works Cited Balabanian, Norman, and Bradley Carlson. Digital Logic Design Principles. New York: Wiley, 2001. Print. Lorente, Nicolas, and C Joachim. Architecture and Design of Molecule Logic Gates and Atom Circuits: Proceedings of the 2nd Atmol European Workshop. Berlin: Springer, 2013. Internet resource. Rafiquzzaman, Mohamed. Fundamentals of Digital Logic and Microcomputer Design. Hoboken, N.J: J. Wiley & Sons, 2005. Print. Wiatrowski, Claude A, and Charles H. House. Logic Circuits and Microcomputer Systems. New York: McGraw-Hill, 1980. Print. Read More