pattpatel-chapter-1CSA.pdf

# Introduction to computing and the book's structure This section introduces the fundamental concept that computers are deterministic systems and outlines the book's layered approach to understanding computing, starting from information representation and progressing to hardware architecture. ### 1.1 The nature of computers * Computers are deterministic systems, meaning they produce the same output for the same input and internal state [1](#page=1). * They are not "electronic geniuses" but rather execute instructions precisely as given, devoid of independent thought [1](#page=1). * A complex computer is built from a systematically interconnected collection of very simple parts [1](#page=1). ### 1.2 Book's approach and structure The book employs a layered approach, starting from foundational concepts and building up to more complex ones, similar to constructing a house from its foundation. The goal is to enable readers to write programs in languages like C and understand the underlying operations of the computer [1](#page=1) [2](#page=2) [3](#page=3). #### 1.2.1 Layer 1: Information representation * All information processed by a computer is represented by sequences of 0s and 1s [1](#page=1). * Examples include the encoding of the letter 'a' as `01100001` and the decimal number 35 as `00100011` [1](#page=1). * Operations, such as addition, are performed on these encoded representations [1](#page=1) [2](#page=2). #### 1.2.2 Layer 2: Electronic components and basic operations * Computers are electronic devices operated by voltages [2](#page=2). * A high voltage represents a 1, and a low voltage (relative to 0 volts) represents a 0 [2](#page=2). * Transistors are the fundamental building blocks that perform operations and store information [2](#page=2). #### 1.2.3 Layer 3: The von Neumann machine and the LC-3 * Larger structures are combined to form the von Neumann machine, a basic model of computer operation [2](#page=2). * The book will study a simple computer called the LC-3 (Little Computer 3), which possesses key characteristics of modern microprocessors like Intel Core and ARM processors, but in a simplified form for educational purposes [2](#page=2). #### 1.2.4 Layer 4: Programming languages * The book progresses to programming the LC-3, first in its native language, then in assembly language [2](#page=2). * Subsequently, it introduces high-level programming concepts using C and C++ [2](#page=2) [3](#page=3). * High-level languages abstract away hardware details, enabling more effective development of complex software [2](#page=2). * The goal is to connect high-level constructs to their underlying LC-3 implementation [3](#page=3). #### 1.2.5 Second half of the book: Advanced programming * Chapters 11-20 delve into advanced programming concepts in C and C++ [2](#page=2). * Topics include variables, operators, control structures, functions, testing, debugging, pointers, arrays, recursion, input/output, and data structures [3](#page=3). * C++ is presented as an evolution of C [3](#page=3). ### 1.3 Two Recurring Themes Two fundamental ideas permeate the book: #### 1.3.1 The notion of abstraction * Abstraction involves simplifying complex systems by hiding underlying details, allowing users to interact with them at a higher level [3](#page=3). * An analogy is telling a taxi driver to go to the airport, rather than providing turn-by-turn directions [3](#page=3). * Abstraction is crucial in various fields, including mathematics, engineering, and business [3](#page=3). * Understanding when abstractions are reliable and when deeper knowledge is needed is essential [20](#page=20). #### 1.3.2 The importance of not separating hardware and software * Hardware and software are deeply interwoven and should not be viewed as entirely separate entities [3](#page=3) [7](#page=7). * Understanding hardware concepts clarifies software concepts, such as how finite word length affects data types in C [7](#page=7). * Conversely, understanding software concepts can illuminate hardware implementations, for instance, the rules for function calls [7](#page=7). * Mastering both hardware and software enhances problem-solving capabilities [7](#page=7). ### 1.4 A computer system A computer system is defined as a combination of software (programs that direct processing) and hardware (which performs the actual processing) [7](#page=7). #### 1.4.1 A brief history of computing * The first electronic computers emerged in the 1940s [8](#page=8). * The ENIAC (Electronic Numerical Integrator and Computer), built in the 1940s, was a large, vacuum-tube-based machine [8](#page=8). * Significant advancements in size, weight, power consumption, and processing speed have occurred since then [10](#page=10) [8](#page=8) [9](#page=9). * Modern smartphones possess computing power millions of times greater than the ENIAC [9](#page=9). * Microprocessors have seen phenomenal improvements in transistor count and operating frequency [10](#page=10). * Much of what appears magical in modern computing, such as natural language understanding, is due to the speed and parallelism of simple operations [10](#page=10). #### 1.4.2 Components of a computer system A computer system typically includes the processor (CPU), keyboard, mouse, monitor, memory, long-term storage (disks, USB drives), input/output devices (printers), and the software [11](#page=11). ### 1.5 Two Very Important Ideas #### 1.5.1 Universality of computational devices * All computers, regardless of speed or cost, are capable of computing the same things if given sufficient time and memory [11](#page=11). * A faster computer performs computations more quickly, but a slower one can achieve the same results eventually [11](#page=11). * More expensive computers do not possess greater computational power than cheaper ones, provided the latter have enough memory [11](#page=11). * Computers are universal computational devices, meaning they can perform any computation that can be described [12](#page=12) [14](#page=14). #### 1.5.2 Transformation of human language to electron behavior * Problems are described in human languages, but solved by electrons moving within the computer [11](#page=11). * A sequence of systematic transformations is necessary to translate human-understandable problems into electrical signals that control electron flow [11](#page=11) [19](#page=19). ### 1.6 Computers as universal computational devices * Unlike specialized machines, modern computers are universal in their computational capabilities [12](#page=12). * Analog machines, which measure physical quantities, have limitations in accuracy [12](#page=12). * Digital machines, which manipulate discrete digits, allow for increased accuracy by adding more digits [12](#page=12). * Early digital machines, like adding machines or abaci, were limited to specific computations [12](#page=12). * The concept of a universal Turing machine, which can simulate any other Turing machine, demonstrates this universality [14](#page=14). * A computer with sufficient memory is equivalent to a universal Turing machine in terms of what it can compute [14](#page=14). ### 1.7 How do we get the electrons to do the work? This section outlines the "Levels of Transformation" required to translate a problem description into actions performed by electrons. Choices at each level impact cost and performance [14](#page=14) [19](#page=19). #### 1.7.1 Natural language statement of the problem * Problems are initially described in natural languages (e.g., English, French) [14](#page=14). * Natural languages are ambiguous and not suitable for precise instruction [14](#page=14). #### 1.7.2 High-level programming language * Natural language descriptions are translated into high-level programming languages (e.g., C, C++) [14](#page=14). * These languages offer a more structured way to express algorithms but still abstract from hardware specifics [14](#page=14) [2](#page=2). #### 1.7.3 Assembly language * High-level languages are compiled into assembly language, which is a more machine-specific symbolic representation [14](#page=14). #### 1.7.4 Instruction Set Architecture (ISA) * Assembly language is translated into the machine code defined by the Instruction Set Architecture (ISA) [14](#page=14). * The ISA specifies the set of commands the processor understands [14](#page=14). * The book uses the LC-3 ISA [19](#page=19). #### 1.7.5 Microarchitecture * The microarchitecture implements the ISA, detailing how the processor's components are organized and interact [14](#page=14) [19](#page=19). * Different microarchitectures can implement the same ISA, with trade-offs in cost, performance, and energy consumption [19](#page=19). #### 1.7.6 Logic circuit * Each element of the microarchitecture is implemented using basic logic circuits [19](#page=19). * There are choices in logic circuit design to balance cost and performance [19](#page=19). #### 1.7.7 Devices * Logic circuits are realized using specific electronic device technologies (e.g., CMOS, NMOS) [19](#page=19). > **Tip:** Understanding these layers of transformation is crucial for comprehending how a high-level program ultimately instructs the electrons within a computer to perform a task [19](#page=19). --- # Key concepts: Abstraction and hardware-software integration This section explores the fundamental concepts of abstraction as a productivity enhancer and the crucial interplay between hardware and software in computer science and engineering. ### 2.1 The notion of abstraction Abstraction is a technique that simplifies interaction with a system by hiding unnecessary details, allowing users to focus on essential aspects and enhancing productivity. It enables dealing with situations at a higher level, making processes more efficient in terms of time and cognitive load. The effectiveness of abstraction relies on the ability to "un-abstract" or deconstruct back to component parts when necessary [3](#page=3) [4](#page=4). **Examples of abstraction:** * Telling a taxi driver to go to the airport, rather than providing step-by-step directions [3](#page=3). * Thinking of transistors as logic gates that operate with 0s and 1s, rather than dealing with varying voltages [5](#page=5). * Designing a computer application using components as abstractions, without getting bogged down in the internal details of each component unless a problem arises [5](#page=5). **Key principles of abstraction:** * It is a critical skill in various fields, including mathematics, physics, engineering, and business [3](#page=3). * It allows for greater efficiency and prevents users from being overloaded with unnecessary details [4](#page=4). * The ability to un-abstract is crucial for troubleshooting and deeper understanding when problems arise [4](#page=4). * The goal is to maintain the highest possible level of abstraction that still allows for effective operation [5](#page=5). **The Bottom Line on Abstraction:** Abstractions significantly improve efficiency and are perfectly adequate when components function correctly and do not need to be integrated into larger systems. However, understanding the components below the abstraction level is vital for debugging and ensuring systems work together harmoniously [5](#page=5). ### 2.2 Hardware vs. software The distinction between hardware and software, with individuals often identifying as either "hardware people" or "software people," can be misleading and is actively discouraged. Hardware refers to the physical computer and its specifications, while software encompasses operating systems and application programs. This separation implies that expertise in one domain comes at the cost of knowledge in the other, creating a metaphorical "wall" between them [5](#page=5) [6](#page=6). The power of abstraction allows for operation at higher levels without constant consideration of underlying layers, boosting productivity. However, being unaware of these underlying layers limits the ability to leverage their nuances when critical [6](#page=6). The recommended approach is to work at the highest available level of abstraction while simultaneously keeping the underlying layers in mind for improved performance. This holistic view, where hardware and software are seen as integrated components, leads to better design and functionality [6](#page=6). **Examples of hardware-software integration:** * **Microprocessor designers** incorporating specialized hardware capabilities (e.g., Intel's MMX instruction set, Motorola's AltiVec) to efficiently process video clips, recognizing the growing demand in software applications [6](#page=6). * **Software designers** understanding hardware capabilities and limitations to create more efficient programs. For instance, the choice of sorting algorithms can significantly depend on the underlying hardware characteristics [6](#page=6). **The Bottom Line on Hardware-Software Integration:** Mastery of both hardware and software makes individuals more capable and effective. This book aims to guide students toward understanding both domains, as each sheds light on the other [7](#page=7). ### 2.3 Interwoven concepts Numerous software concepts are deeply intertwined with hardware concepts, enhancing understanding when studied together: * **Data types** (software) are influenced by the finite word length of the computer (hardware) [7](#page=7). * **Functions** (software) can be tied to their hardware implementation, explaining the rules of function calling [7](#page=7). * **Recursion** (software) can be related to hardware, helping to determine when recursive execution is beneficial [7](#page=7). * **Pointer variables** (software) are better understood when knowledge of computer memory (hardware) is applied, clarifying their use and avoidance [7](#page=7). * **Data structures** (software) are more efficiently manipulated in memory (hardware) with a deeper understanding of computer memory [7](#page=7). > **Tip:** While many terms might be unfamiliar initially, re-reading this section later in the semester can solidify the understanding of how software and hardware topics are deeply interconnected. Most computing problems benefit from solutions developed by individuals capable of understanding and utilizing both hardware and software aspects. A computer system is fundamentally composed of both software that directs information processing and hardware that executes these instructions [7](#page=7). --- # The levels of transformation in computing This section details the systematic transformations required to translate a problem stated in natural language into actions performed by electrons within a computer, progressing through distinct levels of abstraction. ### 3.1 The statement of the problem The initial stage of defining a problem involves using a "natural language," such as English, French, or Japanese. These languages have evolved organically through human communication over centuries. However, natural languages are inherently ambiguous, which makes them unsuitable for direct instruction to a computer. Ambiguity in natural language can arise from context, tone of voice, or multiple possible interpretations of a sentence, as illustrated by the example "Time flies like an arrow". Computers, lacking the ability to infer meaning from context, require precise instructions [15](#page=15). > **Tip:** Understanding the inherent ambiguity of natural language is crucial for appreciating why a more formalized approach is necessary in computing. ### 3.2 The algorithm The first transformation converts a natural language problem description into an algorithm. An algorithm is a step-by-step procedure that is guaranteed to terminate and where each step is precisely stated and executable by a computer. Key properties of an algorithm include [16](#page=16): * **Definiteness:** Each step must be precisely stated, leaving no room for interpretation. A recipe instruction like "stir until lumpy" lacks definiteness [16](#page=16). * **Effective Computability:** Each step must be executable by a computer. An instruction like "take the largest prime number" lacks effective computability, as there is no largest prime number [16](#page=16). * **Finiteness:** The procedure must terminate. For any given problem, multiple algorithms can exist, varying in the number of steps required or the potential for concurrent execution. While more steps might increase total work, concurrency can reduce execution time on parallel processing systems [16](#page=16). > **Example:** An algorithm to sort a list of numbers could be selection sort, insertion sort, or quicksort, each with different step counts and performance characteristics. ### 3.3 The program An algorithm is further transformed into a computer program written in a "mechanical language," known as a programming language. Unlike natural languages, programming languages are invented specifically for instructing computers and are therefore free from ambiguity. Over a thousand programming languages exist, designed for various purposes, such as Fortran for scientific calculations, COBOL for business data processing, Prolog for expert systems, LISP for artificial intelligence, and Pascal for teaching [16](#page=16). Programming languages are categorized into two types: * **High-level languages:** These are further removed from the underlying computer hardware and are often machine-independent, meaning programs written in them can run on different types of computers without modification. Languages like C, C++, Fortran, COBOL, Prolog, LISP, and Pascal are examples of high-level languages [16](#page=16). * **Low-level languages:** These are closely tied to the specific computer hardware. The primary low-level language for a computer is its assembly language [16](#page=16). ### 3.4 The ISA The next transformation involves translating the program into the instruction set of the target computer, known as the Instruction Set Architecture (ISA). The ISA defines the interface between software and hardware, specifying what operations the computer can perform and how to access data [17](#page=17). An analogy for ISA is the interface of an automobile: the pedals, steering wheel, and ignition key are part of the car's "ISA," dictating how a human driver interacts with the car and what the car interprets those actions to mean. Similarly, a computer's ISA defines [17](#page=17): * **Opcodes:** The operations the computer can perform [17](#page=17). * **Operands:** Individual data values used by operations [17](#page=17). * **Data Types:** The representation of operands that the computer can operate on [17](#page=17). * **Addressing Modes:** Mechanisms for locating operands in memory [17](#page=17). The number of opcodes, data types, and addressing modes varies significantly among different ISAs. The x86 ISA, common in PCs, features over 200 opcodes, more than a dozen data types, and over two dozen addressing modes. The ISA also specifies memory organization, including the number of memory locations and the number of bits per location. Prominent ISAs include x86 (Intel, AMD), ARM and THUMB (ARM), POWER and z/Architecture (IBM), and SPARC (Oracle) [17](#page=17) [18](#page=18). Translation from high-level languages to ISA is typically done by a **compiler**, while translation from assembly language to ISA is done by an **assembler** [18](#page=18). > **Tip:** The ISA is a critical abstraction layer that allows for hardware independence at the software level. Different microarchitectures can implement the same ISA. ### 3.5 The microarchitecture The microarchitecture is the implementation of a specific ISA. Continuing the automobile analogy, while all cars share a common ISA (e.g., the brake pedal is always the middle pedal), their microarchitectures (engine type, brake system, fuel efficiency) can differ significantly. Different microarchitectures offer trade-offs in cost, performance, and energy consumption. For instance, the x86 ISA has been implemented by numerous microarchitectures, from the early 8086 to modern processors like Skylake. Computer designers make deliberate choices at this level to balance these factors [18](#page=18) [19](#page=19). > **Example:** Two different processors might implement the same x86 ISA but have vastly different internal designs, leading to different speeds and power usages. ### 3.6 The logic circuit Each component of the microarchitecture is realized using simple logic circuits. At this level, logic designers again make trade-offs between cost and performance. For example, even a basic operation like addition can be implemented using different logic circuit designs, each with varying speeds and costs [19](#page=19). ### 3.7 The devices Finally, each basic logic circuit is implemented based on the requirements of the specific device technology being used. Different technologies, such as CMOS, NMOS, and gallium arsenide circuits, lead to different circuit implementations [19](#page=19). The overall process from a natural language problem statement to the execution by electrons involves these systematic transformations. Each level presents choices that influence the cost and performance of the final computing system. The book aims to describe these transformations, from transistors forming logic circuits, to logic circuits forming microarchitectures, and microarchitectures implementing ISAs, culminating in the translation of a problem description into a program that is then compiled to a target ISA [19](#page=19). --- # Computers as universal computational devices Computers are universal computational devices, meaning they can perform any computable task given sufficient resources, a concept rooted in the theoretical framework of Turing machines. ## 4. Computers as universal computational devices Computers are understood as universal computational devices because they possess the capability to perform any task that is computable, provided they have access to sufficient time and memory. This fundamental characteristic implies that all computers, regardless of their speed, size, or cost, can compute the same set of problems. A faster or more expensive computer might complete computations more quickly or offer enhanced user interfaces, but it cannot solve problems that a slower, cheaper computer is incapable of solving, assuming adequate memory is available for the latter [11](#page=11) [13](#page=13) [14](#page=14). ### 4.1 Digital vs. Analog Machines Historically, calculating machines have existed in two primary forms: analog and digital [12](#page=12). * **Analog machines** perform computations by measuring physical quantities like distance or voltage. An example is a slide rule, which uses logarithmic scales to multiply numbers. A significant limitation of analog machines is the difficulty in increasing their accuracy [12](#page=12). * **Digital machines** perform computations by manipulating a fixed set of digits or letters. This distinction is analogous to analog and digital watches; digital watches offer greater accuracy by displaying time in digits, which can be extended to higher precision (e.g., hundredths of a second) by adding more digits. The document specifies that "computers" in this context refer exclusively to digital machines [12](#page=12). Before modern digital computers, prevalent digital machines included adding machines and the abacus, which were designed for specific tasks like adding integers or sorting data. The key limitation of these specialized machines was their inability to perform computations beyond their designed function; for instance, an adding machine user would need to resort to pencil and paper for multiplication [12](#page=12). ### 4.2 The concept of the Turing machine The foundational idea of a universal computational device is attributed to Alan Turing. In 1937, Turing proposed that all computations could be performed by a theoretical machine now known as a Turing machine [13](#page=13). #### 4.2.1 Definition and purpose of the Turing machine Turing's contribution was a mathematical description of a machine capable of executing any computation. He was motivated by the philosophical problem of defining computation itself. Turing abstracted the actions people perform during computation, such as marking paper or writing symbols based on rules, and specified a mechanism that could replicate these actions. He demonstrated that individual Turing machines could perform specific tasks, like adding or multiplying integers [13](#page=13). * **Black box models of Turing machines:** These models represent Turing machines conceptually, showing inputs and outputs without detailing the internal operations. Figure 1.7 illustrates black box models for machines that add (TADD) and multiply (TMUL) [13](#page=13). * **Turing's thesis:** This thesis posits that every computation can be performed by some Turing machine. While not formally proven, extensive evidence supports its validity. Enhancements to Turing machines have not demonstrated the ability to compute more than the original model [13](#page=13). #### 4.2.2 The universal Turing machine Turing also conceived of a "universal" Turing machine (U) capable of simulating any other Turing machine. This means that by providing U with a description of a specific Turing machine and the necessary input data, U could execute that computation [13](#page=13) [14](#page=14). > **Tip:** The concept of a universal Turing machine is a theoretical precursor to modern programmable computers. It establishes that a single machine, given the right instructions, can perform any task another specialized machine can. For example, to compute $g \cdot (e + f)$, a universal Turing machine U would be provided with descriptions of the Turing machines for addition (TADD) and multiplication (TMUL), along with the inputs e, f, and g. U would then perform the calculation [14](#page=14). Figure 1.8 illustrates this with a black box model of a universal Turing machine (U) that can perform the computation $g \cdot (e + f)$ given TADD, TMUL, and the inputs e, f, and g [14](#page=14). > **Key Insight:** Turing's universal machine provided the first conceptual model of what computers fundamentally do: accept a description of a computation and its data, and then execute it. Both universal Turing machines and modern computers (with unlimited memory) can compute the same set of problems because they are programmable [14](#page=14). ### 4.3 Programmability and universality The programmability of computers is the reason why a large or expensive machine offers no computational advantage over a smaller, cheaper one; the latter is already a universal computational device. Any computation that can be performed by any machine can be performed by a computer, given sufficient time and memory. This universality is a cornerstone of computer science, leading to the study of what computation is and what is fundamentally computable [13](#page=13) [14](#page=14). ### 4.4 Transformation of problems A crucial aspect of computing is the transformation of human-understandable problems, often described in natural language, into the electrical signals that control electron flow within the computer. This transformation involves a sequence of systematic steps developed over decades, enabling computers to execute seemingly complex tasks through simple, underlying operations. The process of "getting the electrons to do the work" is organized into "Levels of Transformation" [11](#page=11) [14](#page=14). --- ## Common mistakes to avoid - Review all topics thoroughly before exams - Pay attention to formulas and key definitions - Practice with examples provided in each section - Don't memorize without understanding the underlying concepts

| Term | Definition | |------|------------| | Abstraction | A technique for simplifying interaction with a system by hiding unnecessary details, allowing focus on essential aspects and enhancing productivity. | | Algorithm | A precise, step-by-step procedure that is guaranteed to terminate, with each step being clearly stated and executable by a computer. | | Assembly Language | A low-level programming language that is closely tied to the specific computer's instruction set architecture, serving as a human-readable representation of machine code. | | Compiler | A translating program that converts code written in a high-level programming language into the instruction set architecture of a specific computer. | | Computer System | A collection of components, including a processor, memory, input/output devices, and software, that work together to perform computations. | | Definiteness | A characteristic of an algorithm ensuring that each step is precisely stated and unambiguous, leaving no room for multiple interpretations. | | Digital Machine | A machine that performs computations by manipulating a fixed, finite set of digits or letters, allowing for increased accuracy by adding more digits. | | Effective Computability | The property of an algorithm where each step can actually be carried out by a computer, without requiring impossible or undefined operations. | | Finiteness | The characteristic of an algorithm that guarantees the procedure will eventually terminate after a finite number of steps. | | High-Level Language | A programming language that is at a considerable distance from the underlying computer hardware, often being machine-independent and designed for programmer convenience. | | Instruction Set Architecture (ISA) | The complete specification of the interface between programs and the underlying computer hardware, defining operations, data types, and addressing modes. | | Logic Circuit | A combination of logic gates used to implement a specific function within a microarchitecture, representing an abstraction for designing computer components. | | Low-Level Language | A programming language that is closely tied to the specific computer's architecture, such as assembly language. | | Mechanical Language | A programming language that was invented for specifying computer instructions and does not suffer from the ambiguity found in natural languages. | | Microarchitecture | The implementation of an Instruction Set Architecture (ISA), detailing the specific design choices and trade-offs made by computer designers regarding cost, performance, and energy consumption. | | Natural Language | A language spoken by humans, such as English, which is often ambiguous and unsuitable for providing precise instructions to a computer. | | Opcode | The part of a computer instruction that specifies the operation to be performed. | | Operand | An individual data value that an operation acts upon. | | Program | A sequence of instructions written in a programming language that a computer can execute to perform a specific task. | | Transistor | A fundamental electronic component that can act as a switch or amplifier, forming the building blocks for logic gates and integrated circuits. | | Turing Machine | A mathematical model of computation proposed by Alan Turing, consisting of an infinite tape, a head that can read and write symbols, and a set of states and transition rules. | | Universal Computational Device | A machine, like a computer or a universal Turing machine, capable of computing anything that can be computed, given sufficient time and memory. |