小土刀

【计算机系统导论】1.2 从模拟到数字

每种技术、思想都有其特定的目的、源源和发展进步的过程。正如上一节所说的那样,计算机最初源于模仿人类的思考过程,却在不断的发展过程中找到了自己新的存在形式。在如今的世界中,计算机已经扮演了举足轻重的角色


前面说到,人类花了近四千年才完成了从人工到机械的转变,那么,从模拟到数字的转变,又需要多久呢?

机械 -> 电子

模拟 -> 数字

但并不是一个完全统一的转变过程。

这一讲主要介绍到 1950 年代,核心是讲明白为什么从模拟转向数字

模拟与数字

Analog and Digital: Different Ways to Measure and Model the World

Our world is a symphony of infinite variations. Long before digital computers existed, engineers built models to simulate those real world nuances.

Analog computers continued this tradition, using mechanical motion or the flow of electricity to model problems and generate answers quickly. They remained the preferred tool until digital computers, based on electronic switches, became fast enough for software to do the same job.

Bush’s Analog Solution

Bush(1890–1974) joined MIT at age 29 as an electrical engineering professor and led the design of the differential analyzer. During World War II, he chaired the National Defense Research Committee and advised President Franklin D. Roosevelt on scientific matters.

Bush’s Analog Solution: The Differential Analyzer

Vannevar Bush was stumped. “I was trying to solve some of the problems of electric circuitry….I was thoroughly stuck because I could not solve the tough equations….”

Bush didn’t abandon his task for lack of a tool. He invented a new tool. In 1931, the MIT professor created a differential analyzer to model power networks, but quickly saw its value as a general-purpose analog computer.

Bush’s Differential Analyzer filled a room with a complicated array of gears and shafts driven by electric motors. Wheel-and-disc “integrators” at its heart could be connected to 18 long, rotating shafts.

Started in 1928 by Bush’s student Harold Hazen, the machine could solve, approximately, an arbitrary sixth-order differential equation. But it had to be laboriously set up for each new problem.

In addition to analyzing power transmission networks, Bush’s analyzer solved problems in physics, seismology, and ballistics. It inspired similar devices in the US, Britain, Europe, the Soviet Union, and Australia.

Bush’s differential analyzer inspired more sophisticated versions. His Rockefeller Differential Analyzer, which secretly calculated firing tables and radar antenna profiles during World War II, has been called “the most important computer in existence in the United States at the end of the war.”

Nordsieck’s Differential Analyzer

Using $700 worth of surplus World War II supplies, Arnold Nordsieck assembled an analog computer in 1950. It was modeled on differential analyzers built since the 1930s—but with key differences.

For instance, Nordsieck’s computer used electrical connections instead of mechanical shafts. And he set himself the priorities of “convenience and simplicity…portability, and economy.” His device’s small size and straightforward engineering satisfied the first three requirements. Its $700 price tag satisfied the fourth.

What Did Nordsieck’s Device Do?

How do you aim artillery, balancing variables of speed, trajectory, friction, and other forces? How do you model a complex natural system like climate, factoring in constantly changing measurements from temperature and humidity to wind speed and direction?

Differential equations are the primary means of using mathematical formulas to describe changing phenomena. Arnold Nordsieck’s electromechanical differential analyzer, like mechanical analyzers that preceded it, solved such differential equations. It provided a powerful tool for engineering, rocketry, physics, economics, and other disciplines that needed to model complex real world conditions.

Technology On a Shoestring

What do you need to build a differential analyzer? Richard Norberg might have answered, “What have you got?”

Norberg, who as a grad student had worked with Arnold Nordsieck on his original analyzer at the University of Illinois, completed a second model at Washington University in St. Louis in 1956…using spare parts.

Choosing Analog

We see history in the rear-view mirror. Earlier inventions often seem merely steps on the path to today’s technology. Yet analog computers weren’t just the ancestors of digital. They were powerful calculating instruments with unique strengths.

Analog computers, which measure continuous values, excel at modeling the physical world. Many engineers preferred analog well into the age of microprocessors and digital computers.

Tech Talk: Analog and Digital Approaches to Modeling

An analog computation simulates a real-world problem. Both mechanical differential analyzers and electronic analog computers solve mathematical equations that model the problem. Each physical component of the computer does one mathematical operation.

The answers aren’t very precise, but the operator can interactively change the model or its parameters and quickly see the consequences. At a time when digital computers were expensive and slow, this combination of low cost and high speed made the analog approach very appealing.

As digital computers became faster, cheaper, and more interactive, however, they could solve the same problems efficiently by programming sequential steps for each mathematical operation—in effect, simulating the simulation. And because digital computers use large numbers to count discrete units, their results are more precise. That precision, and the additional flexibility that comes from having the model created entirely in software, eventually made analog computers mostly obsolete.

Why Are They Called “Analog”?

When you say that Superman flies like an arrow, you’re making an analogy—observing that one thing resembles another. The term “analog” derives from ”analogy.”

General-purpose analog computers represent a real world system with an analogous mathematical model. They then calculate solutions using continuously changing voltages or mechanical motion instead of discrete values of zero and one.

Analog Goes Electronic

The analog computer’s evolution from mechanical to electronic began during World War II. The innovation brought greater computing speed, although that didn’t always make electronic analog computers better than their mechanical forebears.

Nonetheless, by the 1950s electronic machines had largely replaced mechanical. Companies began producing diverse models, and electronic analog computers remained a bedrock of engineering and scientific calculating for a generation.

During World War II, Germany’s V-2 rockets heralded the arrival of a frightening new weapon. The missiles used an op-amp analog computer for their onboard guidance systems, though they still proved too inaccurate to be a serious military threat.

America, recognizing the potential of guided rocketry, launched Project Cyclone immediately after the war. Funded by the U.S. Navy, Project Cyclone used the Reeves Electronic Analog Computer (REAC) developed by Reeves Instruments to simulate, develop, and test guided missile systems.

A commercial version of REAC soon followed, with more than 60 installed by 1950.

Analog On Your Team

Even as digital computers matured, the unique strengths of analog computers remained in demand. And where there is demand, there was, and is, supply.

A new class of electronic analog machines—small, desktop models—blossomed in the 1960s and 1970s. They were widely used alongside other instruments for simulations in aeronautics, mechanical engineering, nuclear physics and other fields. Users selected input values through dials; outputs could be recorded on a plotter or display.

Electronic Associates, Inc. (EAI) led the analog desktop market, competing with Telefunken in Europe, Hitachi in Japan and other manufacturers.

A Key Component: The Operational Amplifier

In electronic analog computers, electrical currents represent numerical values: higher or lower voltage signifies greater or lesser values. Key to this process is the operational amplifier (op-amp), a voltage amplifying circuit.

Combined with other components, op-amps use voltage to add, subtract or multiply by a constant and integrate over time. Op-amps also have diverse uses aside from computers.

When bullets and missiles fly, you need to respond swiftly. During World War II, both sides looked to op-amp technology for solutions.

In America, Bell Labs engineer David Parkinson dreamt one night in 1940 of an anti-aircraft gun using the amplifiers he’d developed for telephone circuits. By 1944, the resulting M9 gun director helped destroy 76% of German V-1 buzz bombs.

In wartime Germany, engineer Helmut Hoelzer used op-amps to guide the V-2 rocket. After the war, Hoelzer’s groundbreaking work provided a foundation for America’s Hermes rocket.

Op-amp Circuit Design

The operational amplifier, or “op-amp” is a key component of an electronic analog computer. Its invention in the early 1940s allowed unwieldy mechanical contraptions to be replaced by silent and speedier electronics.

An op-amp, technically, is a high-gain voltage amplifier with differential inputs. Using appropriate negative feedback, a single op-amp can add or subtract two voltage signals, multiply by a constant, or integrate voltage over time. Stringing together many op-amps lets one compute complicated formulas.

Many analog computers relied on vacuum-tube op-amps, available commercially from George A. Philbrick’s company in 1952. In 1963, Bob Widlar at Fairchild Semiconductor made an op-amp on a single integrated circuit.

Widlar’s 1965 µA709 became a huge commercial success. He later became the analog wizard-in-residence at National Semiconductor, widely known not only for his creative and reliable designs, but also for his colorful personality.

The Best of Both Worlds: Hybrid Computing

Analog and digital computers each offered unique advantages. So the best choice, often, was to use both.

As early as 1954, scientists coupled large digital computers with analog machines. By the late 1950s, many experts saw hybrids as the future of computing. However, as digital computers grew faster, they used software simulation to replicate the advantages of analog. Simulation software remains widespread.

Good executives delegate, assigning different tasks to different employees depending on their strengths. Hybrid computing did likewise, delegating different tasks to analog and digital components.

In the 1950s, Ramo-Wooldridge and Convair coupled digital UNIVAC and IBM machines with analog systems for missile guidance simulation. Most analog manufacturers introduced hybrids by the 1960s, generally assigning calculation of things that vary over time to analog, and logical decision-making based on calculations to digital.

As digital machines became faster, simulation languages gradually replaced analog, ending the hybrid era.

EAI 640 hybrid computing system brochure

Hybrid computing became complex and sophisticated. EAI and other vendors offered software packages that helped set up both the analog and the digital sides.

ENIAC

埃尼阿克的诞生终结了大部分模拟计算机的生路,不过从1950年代到1960年代,由数字电子学控制的混合型模拟计算机依然活跃,之后模拟计算机就应用在部分专业用途上。

In 1942, physicist John Mauchly proposed an all-electronic calculating machine. The U.S. Army, meanwhile, needed to calculate complex wartime ballistics tables. Proposal met patron.

The result was ENIAC (Electronic Numerical Integrator And Computer), built between 1943 and 1945—the first large-scale computer to run at electronic speed without being slowed by any mechanical parts. For a decade, until a 1955 lightning strike, ENIAC may have run more calculations than all mankind had done up to that point.

操作员一般都是女性

ENIAC glowed with an unprecedented 18,000 vacuum tubes. How do you keep so many working simultaneously?

Engineers created strict circuit design guidelines to maximize reliability. They ran extensive tests on components and avoided pushing them to their limits, which included operating vacuum tubes well below their maximum voltages to prolong their life.

The Minds Behind ENIAC

Everybody talks about the weather. Predicting it, however, is another matter, a daunting task requiring vast, complex calculations.

In 1941, John Mauchly, head of physics at Ursinus College, presented a paper suggesting an electronic computer to accomplish that feat. A year later, he joined the Moore School of Electrical Engineering and, with electrical engineer Presper Eckert, drafted a proposal for ENIAC.

To find funding, Mauchly had to shift gears, switching from weather forecasting to ballistics to gain Army backing. Once the project was underway, Eckert, 24, became ENIAC’s head engineer. Mauchly was an idea-generator and booster.

Military Demands, Engineering Solutions

As war became increasingly technological, the U.S. Army created a Ballistic Research Laboratory in the 1930s. Among its many assignments was calculating artillery shell firing tables.

In 1935, the Lab received one of two differential analyzers –mechanical devices to help with the equations. The University of Pennsylvania’s Moore School of Electrical Engineering got the other.

When World War II began, the Army’s “human computers” couldn’t keep up with the mushrooming demand for artillery calculations. The Ballistic Research Lab and Moore School developed ENIAC, an electronic solution to ease that backlog.

Computation Becomes Electronic

World War II acted as midwife to the birth of the modern electronic computer. Unprecedented military demands for calculations—and hefty wartime budgets—spurred innovation.

Early electronic computers were one-of-a-kind machines built for specific tasks. But setting them up was cumbersome and time-consuming. The revolutionary innovation of storing programs in memory replaced the switches and wiring with readily changed software.

People didn’t have computers in the 1930s. Yet they needed them.

Scientists, engineers, businesses, and government agencies faced growing mountains of tedious, repetitive calculations. Nobody’s idea of fun. Calculators and punched cards were widespread, but slow and cumbersome. So inventors around the world—often unaware of each other, yet following parallel paths—tackled the challenge.

Their mechanical devices laid the groundwork for electronic computing.


战争是科学的春药,催生了众多新科技,模拟计算机也在此转变

1930年代后期到1940年代,受到二次大战影响,此一时期被认为是计算机发展史中的混乱时期,战争开启了现代电脑的时代,电子电路、继电器、电容及真空管相继登场,取代机械器件,就连类比计算器也被数字计算器所代替。阿塔那索夫贝理电脑(ABC)、Z3电脑、巨像电脑和埃尼阿克也在手工精心打造下诞生,使用包含继电器或真空管的电路,以打孔卡或打孔带作为输入和主要(非短期)储存媒介。
在这个时期,功能各异的电脑陆续生产,稳定发展。刚开始的时候,没人能想像现代电脑的存在,除了为世人遗忘的巴贝奇计划和艾伦·图灵的数学理论。到了这个时代的后期,电子离散顺序自动计算机登场,成为第一部可储存程式的数字电脑。此一期间的电脑系统,暂存内存使用延迟线存储器迅速崛起,直到1970年代中期,几乎取代其它形式成为最主要的暂存内存。
1936年,图灵发表的研究报告对计算机和计算机科学领域造成巨大冲击,这篇报告主要是为了证明循环处理程式的死角,亦即停机问题的存在。图灵也以算法概念为通用计算机(纯理论器件)作出定义,后来称为图灵机,取代哥德尔渐趋累赘的通用语言。除了内存限制,现代电脑已经具备图灵完全的条件,也就是说,现代电脑的算法执行力已与通用图灵机相当。内存限制有时也被视为一般用途电脑与特殊用途电脑的差别。
一部计算机要实际成为一般用途的电脑,就必须要有像是打孔带之类便于使用的读写器件,而为了要达到多功能多用途,冯·诺伊曼结构下的内存可一并储存程式和资料,当时的电脑差不多都是使用这种架构。理论上这种架构可以应用在全机械的计算机上(像巴贝奇的设计),加上电子学,使得现代电脑的特征──执行速度加快和微型化成为可能。
二次大战时期的电脑发展分为三道平行方向,其中有两方不是被大为忽略,就是被慎重的隐瞒起来,一个是德国科学家楚泽的作品,再则是英国秘密开发的巨像电脑,两者对美国的各项计算机计划都没有太多影响。战后英美计算机科学家在一些将计算机器件实用化方面则有着重要的合作经验。

Konrad Zuse 1941

Konrad Zuse (1910-1995)

Zuse was a brilliant engineer who worked independently to build programmable computers, but his early machines were destroyed in World War II. After the war, his company Zuse KG became a successful computer manufacturer. Zuse was also a prolific painter.

Konrad Zuse was bored. A civil engineering student in Berlin, he hated his job’s tedious calculations. So, as an engineer in 1936, he began assembling metal plates, pins and discarded movie film into what became the Z1—the first of several mechanical computers.

Working on his own, Zuse developed machines with many features of later computers.

The first Bombe is completed 1941

Built as an electromechanical mechanical means of decrypting Nazi ENIGMA-based military communications during World War II, the British Bombe is conceived of by computer pioneer Alan Turing and Harold Keen of the British Tabulating Machine Company. Hundreds of bombes were built, their purpose to ascertain the daily rotor start positions of Enigma cipher machines, which in turn allowed the Allies to decrypt German messages.

Atanasoff-Berry Computer 1942

After successfully demonstrating a proof-of-concept prototype in 1939, Professor John Vincent Atanasoff receives funds to build a full-scale machine at Iowa State College (now University). The machine was designed and built by Atanasoff and graduate student Clifford Berry between 1939 and 1942. The ABC was at the center of a patent dispute related to the invention of the computer, which was resolved in 1973 when it was shown that ENIAC co-designer John Mauchly had seen the ABC shortly after it became functional.

The legal result was a landmark: Atanasoff was declared the originator of several basic computer ideas, but the computer as a concept was declared un-patentable and thus freely open to all. A full-scale working replica of the ABC was completed in 1997, proving that the ABC machine functioned as Atanasoff had claimed. The replica is currently on display at the Computer History Museum.


Mathematician and physicist John Atanasoff, looking for ways to solve equations automatically, took a drive to clear his thoughts in 1937. At a Mississippi River roadhouse he jotted on a napkin the basic features of an electronic computing machine.

Atanasoff’s linear equation-solver, built with graduate student Clifford Berry, could solve a variety of problems but was not programmable.

ENIAC: The First Electronic Computer. Until it Wasn’t.

Being the first electronic computer involved more than bragging rights. It involved money.

ENIAC’s inventors filed for patents in 1947. They were finally issued in 1964, and patent-holder Sperry Rand sought royalties from competitors.

Honeywell and CDC objected, citing prior work by John Atanasoff, who conceived an electronic computer in 1937 and built it in 1939-1942. Significantly, ENIAC inventor John Mauchly had visited Atanasoff in 1941.

In 1967 the dispute landed in court. The ruling, recognizing Atanasoff’s earlier work, revoked Sperry’s patents. So, one of history’s key inventions is owned by…nobody.

Harvard Mark 1 is completed 1944

Howard Aiken (1900-1973)

Aiken, a physicist, was frustrated by the tedious work of solving equations: “All these computational difficulties can be removed by the design of suitable automatic calculating machinery.” A colleague described him as “forceful, self-assured, and formidable,” but “a marvelous teacher.”

(Harvard Mark I/IBM ASCC)

Howard Aiken realized that one way to reduce human error in calculations was to reduce human involvement. In 1937 he proposed an automated calculating machine. IBM and Harvard agreed to build it.

Completed in 1944, Aiken’s “Harvard Mark I” calculator helped design America’s atomic bomb. More sophisticated Mark II, III, and IV versions followed.

Conceived by Harvard physics professor Howard Aiken, and designed and built by IBM, the Harvard Mark 1 is a room-sized, relay-based calculator. The machine had a fifty-foot long camshaft running the length of machine that synchronized the machine’s thousands of component parts and used 3,500 relays. The Mark 1 produced mathematical tables but was soon superseded by electronic stored-program computers.

John von Neumann writes First Draft of a Report on the EDVAC 1945

In a widely circulated paper, mathematician John von Neumann outlines the architecture of a stored-program computer, including electronic storage of programming information and data – which eliminates the need for more clumsy methods of programming such as plugboards, punched cards and paper. Hungarian-born von Neumann demonstrated prodigious expertise in hydrodynamics, ballistics, meteorology, game theory, statistics, and the use of mechanical devices for computation. After the war, he concentrated on the development of Princeton´s Institute for Advanced Studies computer.

The First Generation

John von Neumann with the IAS Computer

Von Neumann persuaded IAS to expand from doing theoretical studies to building a real computer, with meteorology calculations as a key test of its scientific value. The cylinders at the bottom are the Williams-Kilburn memory tubes.

Once the world had seen a stored program computer, the advantages were obvious. Every university, research institute and lab wanted one of its own. But where to get one?

There were no commercial manufacturers of electronic, stored-program computers. If you wanted one, you had to build one. Many of these early machines relied on published designs. Others were developed independently.

Invention and Influence: The Institute for Advanced Study

Like stones tossed in a pond, groundbreaking ideas nurtured at Princeton’s Institute for Advanced Study (IAS) sent ripples through the computer world, inspiring labs and technology companies around the globe.

The IAS project to develop a stored-program computer was initiated in 1946 by mathematician John von Neumann, joined by alumni of the Moore School’s ENIAC project.

The computer was operational by 1951, and the IAS made its design freely available. This “open source hardware” begat similar machines around the world, as well as a host of variations on the IAS theme.

Pilot ACE 1950

ACE Pilot Model

This “pilot” machine, simpler than Turing’s full ACE (Automatic Computing Engine) design, was completed at NPL in 1950. Although built as a test machine, it remained in useful operation for five years.

After his wartime triumphs in code-breaking, Alan Turing joined Britain’s National Physical Laboratory in 1945 to develop electronic computers.

Turing created seven designs. Six remained, as intended, just experimental concepts. Design #5 was built in 1950 as Pilot ACE (Automatic Computing Engine), a precursor to the later full-scale ACE.

Alan Turing (1912-1954)

Turing was a brilliant mathematician, wrote influential papers on logic and artificial intelligence. He committed suicide following a criminal prosecution on charges of homosexuality.


模拟计算机

  • 第一台电子模拟计算机于1946年研制成功
  • 原理是基于不同物理量变化规律在数学描述上的相似性
  • 机器变量是连续变化的电压变量,对于变量的运算是基于电路中电压、电流、元件等电特性的相似运算关系
    • 如电路节点上任一支路电流等于其余各支路电流之和(基尔霍夫定律),这是加法运算的基础
    • 如电容是积累电荷的元件,当电荷流入电容器,电容两端电压增大,它的数学关系表现为电流对时间的积分,这就是实现积分运算的基础
  • 通用电子模拟计算机的组成包括
    • 线性运算部件(比例器、加法器、积分器等)
      • 只要放大倍数足够大,放大器的输出电压与输入电压之间的关系取决于两个电阻之比,并取相反极性。这就是线性运算部件中最简单的比例运算器。
    • 非线性运算部件(函数产生器、乘法器等)
      • 二极管具有单向导通特性,把它接入运算放大器的输入和反馈回路中就能使运算关系呈现非线性特性。这种性质被用来实现平方、正弦、余弦、对数等特定函数特性和限幅、死区、磁滞等典型非线性特性。
      • 乘法器也是一种重要的非线性部件,它可以完成两个变量的相乘。乘法器的类型很多,如机电式乘法器、脉冲调制乘法器、四分之一平方乘法器、混合乘法器等。
    • 控制电路,电源,排题接线板,输出显示与记录装置。
      • 模拟计算机的控制电路主要用于运算部件的状态控制。对于多数运算部件控制的状态只有两种:准备状态(用于运算部件的零位调整)和计算状态(运算状态)。积分器除准备状态和计算状态外还有设置状态(用于给定积分器初始电压)和保持状态(保持各运算部件的输出在该瞬时的数值供检测用)。状态控制是通过一组机电式电子开关的组合实现的。
      • 模拟计算机运算部件的输出和输入,通常是连接到一个集中的排题板上。排题板上连接孔的位置是按照一定的规律排列的,连接孔标以不同的色彩,以便连接时区分部件的类型和功能。现代模拟计算机的排题板都是可更换的,一台模拟计算机可有 8~10块排题板,供使用者在机下进行程序编排。更先进的排题方式是采用电子开关矩阵,开关的个数可以达数万个,通过对开关的控制自动完成排题线的连接。
  • 处理某些问题很快,但是却不够通用
  • 数字计算机快速发展直接宣告了模拟计算机的死亡
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