A Review of Logic Design Theory by N.N. Biswas: How It Covers Both Traditional and Modern Topics of Logic Design
Logic Design Theory by N.N. Biswas: A Comprehensive Guide
Logic design theory is a branch of computer science and engineering that deals with the design and analysis of digital logic circuits. Logic circuits are the building blocks of digital systems, such as computers, microprocessors, memory devices, communication devices, etc. Logic design theory aims to find efficient and reliable ways to implement logic functions using various types of components, such as transistors, diodes, resistors, capacitors, etc.
logic design theory by n.n Biswas
Logic design theory is especially important for very large scale integration (VLSI) technology, which involves the fabrication of millions or billions of transistors on a single chip. VLSI technology enables the development of complex and powerful digital systems, such as microprocessors, microcontrollers, digital signal processors, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), etc. However, VLSI also poses many challenges and issues for logic design, such as speed, power, area, reliability, testability, etc. Therefore, logic design theory needs to address these challenges and issues by developing new methods and techniques that can optimize logic circuits for VLSI.
One of the most comprehensive and authoritative books on logic design theory is Logic Design Theory by N.N. Biswas. N.N. Biswas is a professor of computer science and engineering at the Indian Institute of Technology (IIT) Kharagpur. He has more than 40 years of teaching and research experience in logic design, VLSI design, computer architecture, parallel processing, etc. He has authored several textbooks and research papers on these topics. He has also received many awards and honors for his contributions to the field.
Logic Design Theory by N.N. Biswas covers both the traditional topics of logic design and the various new topics and approaches that address the special problems posed by VLSI. The book is divided into 12 chapters that cover the following topics:
Boolean Functions and Logical Operations
This chapter introduces the basic concepts and definitions of Boolean algebra and switching algebra, which are the mathematical foundations of logic design. Boolean algebra deals with the manipulation of Boolean values (0 or 1) using logical operations (AND, OR, NOT, etc.). Switching algebra deals with the representation and manipulation of switching functions (functions that map binary inputs to binary outputs) using switching variables (variables that can take binary values) and switching operators (operators that perform logical operations on switching variables).
This chapter also discusses the canonical forms and standard representations of Boolean functions, such as minterms, maxterms, sum-of-products (SOP), product-of-sums (POS), etc. These forms and representations are useful for simplifying and minimizing Boolean functions using algebraic methods. The chapter also explains how to perform logical operations on Boolean functions using various properties, such as commutativity, associativity, distributivity, idempotency, complementarity, duality, De Morgan's laws, etc.
The Karnaugh Map
This chapter introduces the Karnaugh map method for simplifying and minimizing Boolean functions. A Karnaugh map is a graphical representation of a Boolean function that shows all possible combinations of input values and their corresponding output values in a tabular form. The rows and columns of a Karnaugh map are labeled with binary codes that represent the input values. The cells of a Karnaugh map contain binary digits that represent the output values.
to use a Karnaugh map to find the minimum sum-of-products or product-of-sums form of a Boolean function by grouping adjacent cells that contain the same output value. These groups are called implicants and the largest possible groups are called prime implicants. The chapter also explains how to handle don't-care conditions (conditions where the output value does not matter) and multiple output functions (functions that have more than one output variable) using a Karnaugh map.
This chapter also discusses the advantages and limitations of the Karnaugh map method. The advantages include its simplicity, intuitiveness, and effectiveness for small-scale problems. The limitations include its difficulty, tediousness, and impracticality for large-scale problems.
Tabular and Computer-Aided Minimization
This chapter introduces the tabular and computer-aided methods for simplifying and minimizing Boolean functions. These methods are more suitable and efficient for large-scale problems than the Karnaugh map method. The most widely used tabular method is the Quine-McCluskey method, which is based on the principle of consensus. The most widely used computer-aided methods are based on algorithms, such as the Espresso algorithm.
This chapter explains how the Quine-McCluskey method works by using a tabular procedure to find all the prime implicants and essential prime implicants of a Boolean function. A prime implicant is an implicant that cannot be further combined with another implicant to form a larger implicant. An essential prime implicant is a prime implicant that covers at least one minterm or maxterm that is not covered by any other prime implicant. The chapter also explains how to select a minimum cover of prime implicants using the Petrick's method or the branch-and-bound method. A minimum cover is a set of prime implicants that covers all the minterms or maxterms of a Boolean function with the minimum number of literals (variables or their complements).
This chapter also explains how to use computer programs and algorithms to perform minimization of Boolean functions. These programs and algorithms can handle large-scale problems more efficiently and effectively than the tabular methods. They can also handle multiple output functions and don't-care conditions more easily. The chapter also discusses some of the features and limitations of these programs and algorithms.
Combinational Logic Design
This chapter introduces the concept and principles of combinational logic design. A combinational logic circuit is a logic circuit that has no memory elements, such as flip-flops or latches. The output of a combinational logic circuit depends only on the current input values, not on the previous input or output values. Combinational logic circuits are used to perform various arithmetic, logical, and data processing operations in digital systems.
This chapter explains how to design a combinational logic circuit from a specification or a Boolean function. The steps involved in designing a combinational logic circuit are: 1) obtain the truth table or the Boolean function that describes the required output for each possible input combination; 2) simplify and minimize the Boolean function using algebraic methods, Karnaugh maps, tabular methods, or computer-aided methods; 3) implement the simplified Boolean function using standard logic gates, such as AND, OR, NOT, NAND, NOR, XOR, etc.; 4) verify the functionality of the logic circuit using simulation tools or hardware testing.
This chapter also explains how to use various types of components and devices to implement combinational logic circuits, such as multiplexers, decoders, encoders, comparators, adders, subtractors, etc. A multiplexer is a device that selects one of several input signals and forwards it to the output. A decoder is a device that converts a binary code into a one-hot code (a code where only one bit is 1 and the rest are 0). An encoder is a device that converts a one-hot code into a binary code. A comparator is a device that compares two binary numbers and produces an output that indicates their equality or inequality. An adder is a device that performs binary addition on two binary numbers. A subtractor is a device that performs binary subtraction on two binary numbers.
, logic diagrams, simulation tools, hardware testing, etc. A truth table is a table that shows the output values for each possible input combination. A Boolean function is a mathematical expression that describes the output value as a function of the input values. A logic diagram is a graphical representation of a logic circuit that shows the connections and symbols of the components and devices. A simulation tool is a software program that mimics the behavior of a logic circuit by using mathematical models and algorithms. A hardware testing is a physical experiment that verifies the functionality of a logic circuit by applying input signals and observing output signals.
Programmable Logic Devices
This chapter introduces the concept and features of programmable logic devices (PLDs). PLDs are logic devices that can be programmed or configured by the user to implement any desired logic function or circuit. PLDs are useful for prototyping, testing, and modifying logic circuits without requiring physical changes or soldering. PLDs are also useful for implementing complex and customized logic circuits that are not available as standard components or devices.
This chapter explains how to use various types of PLDs to implement combinational logic circuits, such as programmable logic arrays (PLAs), programmable array logic (PAL), generic array logic (GAL), etc. A PLA is a PLD that consists of two programmable arrays: one for implementing the product terms (AND array) and one for implementing the sum terms (OR array). A PAL is a PLD that consists of a programmable AND array and a fixed OR array. A GAL is a PLD that consists of a programmable AND array and a programmable OR array.
This chapter also explains how to perform PLA minimization and folding to reduce the number of product terms and inputs required to implement a logic function or circuit. PLA minimization is the process of finding the minimum number of product terms that can cover all the minterms or maxterms of a logic function. PLA folding is the process of sharing common inputs among different product terms to reduce the number of inputs required for a PLA.
This chapter also explains how to use computer-aided design (CAD) tools to design PLDs. CAD tools are software programs that can perform various tasks related to PLD design, such as minimization, folding, programming, simulation, verification, etc.
Sequential Logic Design
This chapter introduces the concept and principles of sequential logic design. A sequential logic circuit is a logic circuit that has memory elements, such as flip-flops or latches. The output of a sequential logic circuit depends not only on the current input values but also on the previous input or output values. Sequential logic circuits are used to store data, perform timing functions, control operations, etc. in digital systems.
This chapter explains how to classify sequential logic circuits into synchronous and asynchronous types. A synchronous sequential circuit is a sequential circuit that operates under the control of a clock signal, which synchronizes the changes in the output values with the changes in the input values. An asynchronous sequential circuit is a sequential circuit that operates without a clock signal, where the changes in the output values depend on the propagation delays of the components and devices.
the state diagram or the state table that describes the required behavior of the sequential circuit; 2) perform state minimization and state assignment to reduce the number of states and assign binary codes to each state; 3) obtain the Boolean functions that describe the output and the next state as functions of the input and the current state; 4) implement the Boolean functions using standard logic gates and memory elements, such as flip-flops or latches; 5) verify the functionality of the sequential circuit using simulation tools or hardware testing.
This chapter also explains how to use various types of components and devices to implement sequential logic circuits, such as flip-flops, latches, registers, counters, shift registers, etc. A flip-flop is a memory element that can store one bit of information and can change its output value only at the rising or falling edge of a clock signal. A latch is a memory element that can store one bit of information and can change its output value whenever the input value changes. A register is a device that can store multiple bits of information and can perform parallel or serial data transfer. A counter is a device that can count the number of clock pulses or input pulses and produce an output that represents the count value. A shift register is a device that can shift the data stored in it to the left or right by one or more positions.
State Minimization and Assignment
This chapter introduces the concept and methods of state minimization and assignment for sequential logic design. State minimization is the process of finding the minimum number of states that can perform the same function as the original sequential circuit. State assignment is the process of assigning binary codes to each state in a sequential circuit.
This chapter explains how to perform state minimization using equivalence relations, partitions, implication charts, etc. An equivalence relation is a relation that divides a set of elements into disjoint subsets such that any two elements in the same subset are equivalent and any two elements in different subsets are not equivalent. A partition is a set of disjoint subsets that covers the entire set of elements. An implication chart is a matrix that shows the implications between pairs of states in a sequential circuit.
This chapter also explains how to perform state assignment using heuristic methods, binary encoding, one-hot encoding, etc. A heuristic method is a method that uses some rules or criteria to guide the decision making process without guaranteeing an optimal solution. A binary encoding is a method that assigns binary codes to each state such that each bit position represents a different attribute or property of the state. A one-hot encoding is a method that assigns binary codes to each state such that only one bit is 1 and the rest are 0.
Finite State Machines
This chapter introduces the concept and types of finite state machines (FSMs). An FSM is a model of computation that consists of a finite set of states, a finite set of inputs, a finite set of outputs, and a transition function that defines how the FSM changes its state and produces its output based on its input. FSMs are widely used to model the behavior of systems or applications that have discrete inputs and outputs and can be in one of a finite number of states.
the inputs and outputs of the system or application; 2) identify the states and transitions of the system or application; 3) draw a state diagram or a state table that represents the FSM; 4) verify and validate the FSM using simulation tools or formal methods.
This chapter also explains how to design an FSM from a specification or a word description. The steps involved in designing an FSM are: 1) understand the specification or the word description and identify the inputs, outputs, states, and transitions of the FSM; 2) draw a state diagram or a state table that represents the FSM; 3) perform state minimization and state assignment to optimize the FSM; 4) implement the FSM using sequential logic circuits or PLDs; 5) verify and validate the FSM using simulation tools or hardware testing.
This chapter also explains how to classify FSMs into two types: Moore machines and Mealy machines. A Moore machine is an FSM where the output depends only on the current state. A Mealy machine is an FSM where the output depends on both the current state and the current input.
Testing and Fault Diagnosis
This chapter introduces the concept and objectives of testing and fault diagnosis in logic design. Testing is the process of applying input signals to a logic circuit and observing output signals to determine whether the logic circuit performs its intended function correctly. Fault diagnosis is the process of locating and identifying the faults that cause a logic circuit to malfunction.
This chapter explains what are the challenges and objectives of testing and fault diagnosis in logic design. The challenges include the complexity and size of logic circuits, the variety and unpredictability of faults, the cost and time of testing and diagnosis, etc. The objectives include finding all possible faults, minimizing test vectors, maximizing fault coverage, minimizing diagnosis time, etc.
This chapter also explains what are the types and models of faults that can occur in logic circuits. Faults are defects or errors that cause a logic circuit to deviate from its intended behavior. Faults can be classified into two types: permanent faults and transient faults. Permanent faults are faults that persist in a logic circuit until they are repaired or replaced. Transient faults are faults that occur randomly and temporarily in a logic circuit due to external factors, such as noise, interference, radiation, etc. Faults can also be modeled using various methods, such as stuck-at faults, bridging faults, open faults, delay faults, etc.
This chapter also explains how to perform fault detection using test vectors, test patterns, test generation algorithms, etc. A test vector is a set of input values that is applied to a logic circuit to observe its output values. A test pattern is a sequence of test vectors that is applied to a logic circuit to observe its output values. A test generation algorithm is an algorithm that generates test vectors or test patterns for a given logic circuit or function.
the behavior of a logic circuit under the presence of faults and compares it with the expected behavior. Fault simulation can be used to determine whether a test vector or a test pattern can detect a fault or not. Fault equivalence is a property that states that two faults are equivalent if they produce the same faulty output for every possible input. Fault equivalence can be used to reduce the number of faults that need to be considered for testing and diagnosis. Fault dominance is a property that states that one fault dominates another fault if it can be detected by every test vector or test pattern that can detect the other fault. Fault dominance can be used to eliminate redundant faults that do not need to be considered for testing and diagnosis.
Design for Testability
This chapter introduces the concept and techniques of design for testability (DFT) in logic design. DFT is the process of designing or modifying a logic circuit to make it easier and cheaper to test and diagnose. DFT aims to improve the testability and diagnosability of a logic circuit by increasing its fault coverage, reducing its test vectors, simplifying its test generation, etc.
This chapter explains what are the techniques and methods for DFT, such as scan design, built-in self-test (BIST), level-sensitive scan design (LSSD), etc. Scan design is a technique that inserts scan paths or scan chains into a logic circuit to make it possible to control and observe the internal states of the circuit. Scan paths or scan chains are sequences of flip-flops or latches that can be connected in series and accessed through scan inputs and scan outputs. Scan design can be used to apply test vectors or test patterns to a logic circuit without requiring complex input signals or output observations.
BIST is a technique that incorporates testing and diagnosis capabilities into a logic circuit itself. BIST consists of three compone