Combinational Circuit

10 Key excerpts on "Combinational Circuit"

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  Transistor Switching and Sequential Circuits

  • John J. Sparkes(Author)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  A Combinational Circuit is one whose output at any given time is a function only of its inputs at that time. Gates are typical examples. A sequential circuit is one whose output at any given time is a function not only of inputs at that time, but also of previous inputs which have since been removed. A sequential circuit usually contains Combinational Circuits. Counters, control circuits, etc., are examples of sequential circuits. Since sequential cir-cuits take note of inputs in the past, they must contain some form of memory; that is to say, the information imparted by the input must remain after the input is removed. The problems of the design of both types of circuit are dis-cussed in the next few chapters. But first the mathematical pro-cedure used in the description of these circuits, namely Boolean algebra, will be briefly described. Only the most elementary aspects of the algebra are required in this book. CHAPTER 4 Combinational Circuits Boolean Algebra Boolean Algebra is an algebra in which the variables can have one of only two possible values. The two values can stand for the truth or falsehood of a statement, the states of a switch (open or closed), the presence of one of two voltage levels, etc. The two values of a variable A, say, are usually written 1 or 0. Since A can have only two values, the complement of A, namely not A or Ä, is also an important variable. If A = l 9 Ä=0, or i f ^ = 0 , ^ = l . In this book the variables refer to voltage levels and any Boo-lean equations we consider relate the voltage of one node or ter-minal to the voltages of other nodes. Thus Z=A means that nodes Z and A are at the same voltage ; both 6 V, say, or both zero volts. In Boolean notation, if we call one voltage level 1 and the other 0, then Z=A means that if Z = l , A = l and that if Z=0, ,4=0. Similarly Ζ—Ά means that when the voltage of Z is 6 V, the voltage of A is zero, and vice versa.

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  Foundation of Digital Electronics and Logic Design

  • Subir Kumar Sarkar, Asish Kumar De, Souvik Sarkar(Authors)
  • 2014(Publication Date)
  • Jenny Stanford Publishing

    (Publisher)

  The branch of electronics that deals with the digital devices, circuits, and systems is called digital electronics . The digital circuits are mainly of two different types—combinational and sequential circuits. We shall describe the combinational digital circuit first and then the Figure 1.1 A digital circuit (combinational). Essential Characteristics of Digital Circuits 3 sequential circuits. A Combinational Circuit is a logic circuit in which the output of the circuit at any instant of time is depends totally on the inputs present at that time only. Figure 1.1 represents the block diagram of the Combinational Circuit: In general, a Combinational Circuit consists of “ n ” input variables, logic gates, and “ m ” output variables. The logic gates of the Combinational Circuits acknowledge signals from the inputs and generate the output signal. The Combinational Circuit in the process transforms binary information from the given input data to the required output data. For n input variables, the number of maximum input combination will be 2 n . It is important to remember that for each possible input combination, there is only one possible output combination. The detailed description of the circuit will be given in the due course. However, the design of Combinational Circuits starts from the verbal outline of the problem and ends in a set of Boolean function or in a logic circuit diagram. 1.2 Advantages of Digital System The advantages of digital system are as follows: 1. Its basic components are highly reliable. 2. It is low cost. 3. It is small in size. 4. It is light weight. 5. It consumes less power. 6. It is faster in operation. 7. It is durable. 8. It requires number heating element, since it is based on field emission. 9. It is reasonably immune to noise. 1.3 Essential Characteristics of Digital Circuits The advantages of a digital system are due to the advent of improved integrated circuit technology.

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  Digital Logic and Microprocessor Design with Interfacing, International Edition

  • Enoch Hwang(Author)
  • 2017(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  65 Control Signals Status Signals MUX '0' Data Inputs Data Outputs Datapath ALU Register ff 8 8 8 Output Logic Control Inputs Control Outputs Control Unit Next-state Logic State Memory Register ff C H A P T E R 3 Combinational Circuits Copyright 2018 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-202 66 CHAPTER 3 Combinational CircuitS Digital circuits, regardless of whether they are part of the control unit or the datapath, are classified as either one of two types: combinational or sequential. Combinational Circuits are digital circuits where the outputs of the circuit are dependent only on the current inputs. In other words, a Combinational Circuit is able to produce an output simply from knowing what the current input values are. Sequential circuits , on the other hand, are circuits whose outputs are dependent on not only the current inputs, but also on all of the past inputs. Therefore, in order for a sequential circuit to produce an output, it must know the current input and all past inputs. Because of their dependency on past inputs, sequential circuits must contain memory elements in order to remember the history of past input values. Combinational Circuits do not need to know about past inputs, and therefore, do not require any memory elements to remember its history. A “large” digital circuit may contain both Combinational Circuits and sequential cir-cuits. However, since both Combinational Circuits and sequential circuits are digital circuits, therefore, they use the same basic building blocks—the AND , OR , and NOT gates. What makes them different is in the way the gates are connected. The car security system from Section 2.11 is an example of a Combinational Circuit. In the example, the siren is turned on when the master switch is on and someone opens the door. If you close the door, then the siren will turn off immediately.

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  Digital Electronic Circuits

  Principles and Practices

  • Shuqin Lou, Chunling Yang(Authors)
  • 2019(Publication Date)
  • De Gruyter

    (Publisher)

  4 Combinational logic circuits 4.1 Introduction In Chapters 2 and 3, fundamental mathematical tool and basic logic gates were introduced to analyze and design digital circuits. Basic logic gates can be combined to form various types of logic circuits with different functions: comparison, encoding, decoding, counting, storage, and so on. Generally, logic circuits are divided into two categories: combinational logic circuits and sequential logic circuits . When logic gates are connected together to form a specified output for certain specified combi-nation of input variables and no storage involved, the resulting circuit is in the category of combinational logic circuits. In a Combinational Circuit, outputs solely depend on current inputs. While in a sequential logic circuit, outputs depend not only on current inputs but also on previous inputs. This chapter introduces the analysis and design of logic circuits with logic gates. Races and hazards in a combi-national logic circuit are also discussed. With the rapid development of integrated circuit technology, methods of construct-ing digital circuits also evolve. Currently, there are two methods to implement a more complicated digital circuit. One is to construct a specified logic circuit with the universal integrated chips that mainly involve medium-scale integration (MSI) and large-scale integration (LSI) chips. The other is to implement a specified integrated logic circuit with programmable logic device (PLD) by electronic design automation software. This chapter also introduces several types of MSI combinational logic circuits, including adders, decoders, encoders, multiplexers, and their application for design-ing a more complicated logic circuit. The commonly used hardware description language (HDL), such as Verilog HDL, and typical Verilog HDL descriptions of commonly used MSI are also introduced.

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  Fundamentals of Digital Logic and Microcontrollers

  • M. Rafiquzzaman(Author)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  Chapter 4 Combinational Logic

  4.1 Basic Concepts

  Digital logic circuits can be classified into two types: combinational and sequential. A Combinational Circuit is designed using logic gates in which application of inputs generates the outputs at any time. An example of a Combinational Circuit is an adder, which produces the result of addition as output upon application of the two numbers to be added as inputs.

  A sequential circuit, on the other hand, is designed using logic gates and memory elements known as flip-flops. Note that the flip-flop is a one-bit memory. A sequential circuit generates the circuit outputs based on the present inputs and the outputs (states) of the memory elements. The sequential circuit is basically a Combinational Circuit with memory. Note that a Combinational Circuit does not require any memory (flip-flops),whereas sequential circuits require flip-flops to remember the present states. A counter is a typical example of a sequential circuit. To illustrate the sequential circuit, suppose that it is desired to count in the sequence 0, 1, 2,3, 0, 1,… and repeat. In binary, the sequence is 00, 01, 10, 11, 00, 01, …, and so on. This means that a two-bit memory using two flip-flops is required for storing the two bits of the counter because each flip-flop stores one bit. Let us call these flip-flops with outputs A and B. Note that initially A = 0 and B = 0. The flip-flop changes outputs upon application of a clock pulse. With appropriate inputs to the flip-flops and then applying the clock pulse, the flip-flops change the states (outputs) to A = 0, B = 1. Thus, the count to 1 can be obtained. The flip-flops store (remember) this count. Upon application of appropriate inputs along with the clock, the flip-flops will change the status to A = 1, B = 0; thus, the count to 2 is obtained. The flip-flops remember (store) the present value of the count at the outputs until a common clock pulse is applied to the flip-flops. The inputs to the flip-flops are manipulated by a Combinational Circuit based on A and B as inputs. For example, consider A = 1, B = 0. The inputs to the flip-flops are determined in such a way that the flip-flops change the states at the clock pulse to A = 1, B

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  Electronic Logic Circuits

  • J. Gibson(Author)
  • 2013(Publication Date)
  • Routledge

    (Publisher)

  2 Basic elements of combinational logic

  Systems constructed so that all the inputs and outputs can only take either one of two allowed states were introduced in Chapter 1 and termed logic systems or circuits. If each output of such a system depends only on the present states of the inputs to the circuit it is called a combinational logic circuit. In a combinational system there is no dependence of one output on the other outputs. Also input states which have occurred previously have no influence on the circuit behaviour. An alternative way of stating this last fact is that the order in which the inputs are applied to the circuit does not affect its final output. Such a system is shown schematically in Fig. 2.1 .

  Fig. 2.1 Combinational logic network

  In the general case illustrated by Fig. 2.1 there are n inputs i1 , i2 , i3 , …, in and m outputs or results r1 , r2 , r3 , …, rm ; each input may take either one of the two logic states and the outputs are also restricted to these logic levels. The actual level at a particular output at any time depends on the logic states present at all of the inputs at that instant in time.

  It is assumed that as soon as any input changes then the outputs change immediately to the levels which correspond to the new input conditions. Any real circuit will take a finite time to operate; this time is called the propagation delay and it may be neglected in most simple applications of combinational logic circuits.

  2.1 Truth tables

  Detailed examination of the general case of a system with a large number of outputs is not necessary. It is sufficient to consider the case of a system with several inputs and a single output, R. The general case of a circuit with m outputs is just m separate single output circuits which all have the same inputs connected to them; i.e. all the circuits have the same n inputs but each has a different output. Figure 2.2

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  Principles of Verilog Digital Design

  • Wen-Long Chin(Author)
  • 2022(Publication Date)
  • CRC Press

    (Publisher)

  5 Combinational Circuits

  DOI: 10.1201/​9781003187196-5

  Combinational and sequential logics are two essential components for the RTL design. A Combinational Circuit consists of logic gates whose outputs at any time are determined directly from the present combination of inputs without regard to previous inputs and/or outputs, as shown in Figure 5.1 . Therefore, there is no notion of storage of information or dependence on values at previous times. There is no clock control as well. Many sophisticated logical functions are realized by Combinational Circuits.

  Figure 5.1:

  Combinational Circuits.

  First, dataflow, behavioral, and structural descriptions of Combinational Circuits are presented in this chapter. Next, basic building blocks of Combinational Circuits, such as arithmetic and logic units, together with their RTL codes, are introduced. The logic units include multiplexer, demultiplexer, comparator, shifter and rotator, encoder, priority encoder, decoder, and bubble sorting, and arithmetic units consist of half adder, full adder, arithmetic logic unit, carry look-ahead adder, and complex multiplier. Finally, several design issues, including overflow detection, bit width design, and saturation arithmetic, are discussed thoroughly.

  5.1 DATAFLOW DESCRIPTION

  Continuous assignment is the most fundamental construct to describe a combinational logic. The continuous assignment is used to represent a combinational logic circuit that can be conveniently represented by an equation or Boolean equation. During simulations, continuous assignments execute whenever their expressions on the right-hand side change. As its name implies, the execution is immediate and its effect is that the output on the left-hand side of the expression is updated promptly once inputs change. Such a behavior is like that of the Combinational Circuit. For example,

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  Logic Designer's Handbook

  Circuits and Systems

  • E. A. Parr(Author)
  • 2013(Publication Date)
  • Newnes

    (Publisher)

  CHAPTER 3 Combinational Logic 3.1 Introduction The simplest logic systems are those which do not involve counters or storage elements. Such systems have several inputs and one or more outputs, and the output state(s) are uniquely defined for every combination of inputs. These logic systems are known as 'combina-tional logic' or 'static logic' systems and are constructed solely from logic gates. Logic Q Fig. 3.1 Combinational logic block diagrams, (a) Generalized problem, (b) Separate circuits, (c) One circuit. A combinational logic system can therefore be represented by fig. 3.1a. We have η inputs l tol n and ζ outputs 0 to O z . Between them there is a circuit of logic gates such that the outputs relate to the inputs in the required manner. In systems with multiple outputs it is usually more convenient (and simpler) to consider each output separately as in fig. 3.1b. A combinational logic system can therefore be constructed as a collection of circuits similar to fig. 3.1c where we have η inputs and one output. The state of the output is determined solely by the state of the inputs. Combinational logic 51 Fig. 3.2 System not using ' A L L ' input states. Not all the possible input conditions might be used, however. In fig. 3.2 we have a storage tank with four level switches ABCD as inputs to a combinational logic circuit. For four inputs there are 16 possible combinations. Except for fault conditions, the designer of this system need only consider five input states: D c Β A 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 It should be noted, though, that a combinational logic will give 'some' output for any input state, and the cautious designer would check that nothing untoward occurs if, say, the input state A = 1, B = 0, C = 1 , D = 1 appeared due to a switch failure. This chapter is concerned with the design of combinational logic circuits. Very few real-life systems are purely static by nature; most involve storage, feedback or counters.

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  Computers and Microprocessors

  Made Simple

  • George H. Olsen, Ian Burdess(Authors)
  • 2016(Publication Date)
  • Made Simple

    (Publisher)

  They are being used increasingly in consumer products, such as washing machines, sewing machines, toys and television games as well as scientific applications for data acquisition and control. This shift away from the traditional markets has, to a large extent, been due to the evolution and development of the basic logic gates used in their construction. Unlike analogue systems, the digital computer is constructed entirely of switching devices capable of assuming only two states, ON and OFF. As the demands for computers have grown and new markets have opened up, the semiconductor device manufacturers have responded by increasing the speed and reducing the size of the basic logic circuits. A majority of the systems in use today is now based upon the popular transistor-transistor logic (TTL) NAND gate. By using these TTL NAND gates, it is possible to design and construct a logic circuit capable of making decisions based upon the current state of the input signals. These combinational logic circuits may be used to perform such elementary tasks as checking the door interlocks of an automatic washing machine before the wash cycle starts, or they may be used to construct a com-plex and high-speed arithmetic unit of a computer capable of adding numbers together at the rate of hundreds of thousands per second. Combinational logic circuits are, however, incapable of learning by experi-ence and always respond to a given situation in exactly the same manner. Based upon the same TTL NAND gates, but by incorporating feedback, it is possible to construct a circuit which can take into account its past experience. These systems, referred to as sequential logic systems, are very important in computers as they can be used to store information and count events as they occur. Finally, at the centre of any computer is a unit which is capable of perform-ing arithmetic calculations at very high speed.

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  Sequential Logic

  Analysis and Synthesis

  • Joseph Cavanagh(Author)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  Combinational logic is used extensively to represent the next-state function and the output function for both synchronous and asynchronous sequential machines. This chapter on combinational logic has been presented as a review of basic anal-ysis and synthesis techniques. Included was a cursory review of number systems and number representations. Boolean algebra was introduced which provides the basic mathematical tools to analyze and synthesize various switching networks. Karnaugh maps and map-entered-variables were presented as one method of minimizing bool-ean functions with up to five variables. For functions containing more than five vari-ables, the Quine-McCluskey algorithm is a preferred method to obtain a minimal sum- 68 Chapter 1 Review of Combinational Logic of-products expression. Combinational logic macros such as, multiplexers, de-coders, encoders, and comparators provide additional flexibility in synthesiz-ing combinational networks. Storage elements such as, SR latches, D , JK , and T flip-flops were also reviewed, since they have a pivotal usage in both syn-chronous sequential machines and asynchronous sequential machines. Finally, a review of PLDs was presented illustrating a hardware programmable ap-proach to combinational logic synthesis. Inputs X i n m p Outputs Z i AND array OR array (a) x 1 x 2 x 1 x 1 ' x 2 x 2 ' AND array OR array (Programmable) x 3 x 3 ' x 3 x 1 x 1 ' x 2 x 2 ' x 3 x 3 ' (b) × × × × × × (Programmable) × × × × × × × × × × × × × z 2 z 1 z 3 z 4 Figure 1.46 Basic organization of a PLA; (a) block diagram; and (b) imple-mentation using three inputs and four outputs.

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