Home Random Page



Binary Representation

Hollerith's machine though had limitations. It was strictly limited to tabulation. The punched cards could not be used to direct more complex computations. In 1941, Konrad Zuse (Zuse died in January of 1996), a German who had developed a number of calculating machines, released the first programmable computer designed to solve complex engineering equations. The machine, called the Z3, was controlled by perforated strips of discarded movie film. As well as being controllable by these celluloid strips, it was also the first machine to work on the binary system, as opposed to the more familiar decimal system.

The binary system is composed of 0s and 1s. A punch card with its two states--a hole or no hole-- was admirably suited to representing things in binary. If a hole was read by the card reader, it was considered to be a 1. If no hole was present in a column, a zero was appended to the current number. The total number of possible numbers can be calculated by putting 2 to the power of the number of bits in the binary number. A bit is simply a single occurrence of a binary number--a 0 or a 1. Thus, if you had a possible binary number of 6 bits, 64 different numbers could be generated. (2^(n-1))

Binary representation was going to prove important in the future design of computers which took advantage of a multitude of two-state devices such card readers, electric circuits which could be on or off, and vacuum tubes.

Harvard Mark I

By the late 1930s punched-card machine techniques had become so well established and reliable that Howard Aiken, in collaboration with engineers at IBM, undertook construction of a large automatic digital computer based on standard IBM electromechanical parts. Aiken's machine, called the Harvard Mark I, handled 23-decimal-place numbers (words) and could perform all four arithmetic operations; moreover, it had special built-in programs, or subroutines, to handle logarithms and trigonometric functions. The Mark I was originally controlled from pre-punched paper tape without provision for reversal, so that automatic "transfer of control" instructions could not be programmed. Output was by card punch and electric typewriter. Although the Mark I used IBM rotating counter wheels as key components in addition to electromagnetic relays, the machine was classified as a relay computer. It was slow, requiring 3 to 5 seconds for a multiplication, but it was fully automatic and could complete long computations without human intervention. The Harvard Mark I was the first of a series of computers designed and built under Aiken's direction.

Alan Turing

Meanwhile, over in Great Britain, the British mathematician Alan Turing wrote a paper in 1936 entitled On Computable Numbers in which he described a hypothetical device, a Turing machine, that presaged programmable computers. The Turing machine was designed to perform logical operations and could read, write, or erase symbols written on squares of an infinite paper tape. This kind of machine came to be known as a finite state machine because at each step in a computation, the machine's next action was matched against a finite instruction list of possible states.

The Turing machine pictured here above the paper tape, reads in the symbols from the tape one at a time. What we would like the machine to do is to give us an output of 1 anytime it has read at least 3 ones in a row off of the tape. When there are not at least three ones, then it should output a 0. The reading and outputting can go on infinitely. The diagram with the labelled states is known a state diagram and provides a visual path of the possible states that the machine can enter, dependent upon the input. The red arrowed lines indicate an input of 0 from the tape to the machine. The blue arrowed lines indicate an input of 1. Output from the machine is labelled in neon green.

The Turing Machine

The machine starts off in the Start state. The first input is a 1 so we can follow the blue line to State 1; output is going to be 0 because three or more ones have not yet been read in. The next input is a 0, which leads the machine back to the starting state by following the red line. The read/write head on the Turing machine advances to the next input, which is a 1. Again, this returns the machine to State 1 and the read/write head advances to the next symbol on the tape. This too is also a 1, leading to State 2. The machine is still outputting 0's since it has not yet encountered three 1s in a row. The next input is also a 1 and following the blue line leads in to State 3, and the machine now outputs a 1 as it has read in at least 3 ones. From this point, as long as the machine keeps reading in 1s, it will stay in State 3 and continue to output 1s. If any 0s are encountered, the machine will return to the Start state and start counting 1s all over.

Turing's purpose was not to invent a computer, but rather to describe problems which are logically possible to solve. His hypothetical machine, however, foreshadowed certain characteristics of modern computers that would follow. For example, the endless tape could be seen as a form of general purpose internal memory for the machine in that the machine was able to read, write, and erase it--just like modern day RAM.


Back in America, with the success of Aiken's Harvard Mark-I as the first major American development in the computing race, work was proceeding on the next great breakthrough by the Americans. Their second contribution was the development of the giant ENIAC machine by John W. Mauchly and J. Presper Eckert at the University of Pennsylvania. ENIAC (Electrical Numerical Integrator and Computer) used a word of 10 decimal digits instead of binary ones like previous automated calculators/computers. ENIAC also was the first machine to use more than 2,000 vacuum tubes, using nearly 18,000 vacuum tubes. Storage of all those vacuum tubes and the machinery required to keep the cool took up over 167 square meters (1800 square feet) of floor space. Nonetheless, it had punched-card input and output and arithmetically had 1 multiplier, 1 divider-square rooter, and 20 adders employing decimal "ring counters," which served as adders and also as quick-access (0.0002 seconds) read-write register storage.

The executable instructions composing a program were embodied in the separate units of ENIAC, which were plugged together to form a route through the machine for the flow of computations. These connections had to be redone for each different problem, together with presetting function tables and switches. This "wire-your-own" instruction technique was inconvenient, and only with some license could ENIAC be considered programmable; it was, however, efficient in handling the particular programs for which it had been designed. ENIAC is generally acknowledged to be the first successful high-speed electronic digital computer (EDC) and was productively used from 1946 to 1955. A controversy developed in 1971, however, over the patentability of ENIAC's basic digital concepts, the claim being made that another U.S. physicist, John V. Atanasoff, had already used the same ideas in a simpler vacuum-tube device he built in the 1930s while at Iowa State College. In 1973, the court found in favor of the company using Atanasoff claim and Atanasoff received the acclaim he rightly deserved.

John von Neumann

In 1945, mathematician John von Neumann undertook a study of computation that demonstrated that a computer could have a simple, fixed structure, yet be able to execute any kind of computation given properly programmed control without the need for hardware modification. Von Neumann contributed a new understanding of how practical fast computers should be organized and built; these ideas, often referred to as the stored-program technique, became fundamental for future generations of high-speed digital computers and were universally adopted. The primary advance was the provision of a special type of machine instruction called conditional control transfer--which permitted the program sequence to be interrupted and reinitiated at any point, similar to the system suggested by Babbage for his analytical engine--and by storing all instruction programs together with data in the same memory unit, so that, when desired, instructions could be arithmetically modified in the same way as data. Thus, data was the same as program.

As a result of these techniques and several others, computing and programming became faster, more flexible, and more efficient, with the instructions in subroutines performing far more computational work. Frequently used subroutines did not have to be reprogrammed for each new problem but could be kept intact in "libraries" and read into memory when needed. Thus, much of a given program could be assembled from the subroutine library. The all-purpose computer memory became the assembly place in which parts of a long computation were stored, worked on piecewise, and assembled to form the final results. The computer control served as an errand runner for the overall process. As soon as the advantages of these techniques became clear, the techniques became standard practice. The first generation of modern programmed electronic computers to take advantage of these improvements appeared in 1947.

This group included computers using random access memory (RAM), which is a memory designed to give almost constant access to any particular piece of information. These machines had punched-card or punched-tape input and output devices and RAMs of 1,000-word. Physically, they were much more compact than ENIAC: some were about the size of a grand piano and required 2,500 small electron tubes, far fewer than required by the earlier machines. The first- generation stored-program computers required considerable maintenance, attained perhaps 70% to 80% reliable operation, and were used for 8 to 12 years. Typically, they were programmed directly in machine language, although by the mid-1950s progress had been made in several aspects of advanced programming. This group of machines included EDVAC and UNIVAC, the first commercially available computers.


EDVAC (Electronic Discrete Variable Automatic Computer) was to be a vast improvement upon ENIAC. Mauchly and Eckert started working on it two years before ENIAC even went into operation. Their idea was to have the program for the computer stored inside the computer. This would be possible because EDVAC was going to have more internal memory than any other computing device to date. Memory was to be provided through the use of mercury delay lines. The idea being that given a tube of mercury, an electronic pulse could be bounced back and forth to be retrieved at will--another two state device for storing 0s and 1s. This on/off switchability for the memory was required because EDVAC was to use binary rather than decimal numbers, thus simplifying the construction of the arithmetic units.

Date: 2015-12-18; view: 478

<== previous page | next page ==>
The First Mechanical Calculator | Technology Advances
doclecture.net - lectures - 2014-2019 year. Copyright infringement or personal data (0.003 sec.)