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1. AUTOMATIC DIGITAL COMPUTERS
Atlas 1 is a very fast, automatic digital computer with built-in time-sharing facilities enabling a considerable number of problems to be processed simultaneously. This manual is intended for those who will prepare programs giving the machine detailed instructions for the step-by-step solution of individual problems. It is likely that they will have some previous knowledge of computers: should the ideas outlined in this chapter be unfamiliar, the reader is advised to consult an introductory text for further clarification.
1.2 Electronic Computers
The application of electronics has led to the development of the modern high-speed computer; we must distinguish two types of electronic computers:-
Analogue computers represent quantities by some analogous physical quantity and solve problems by working with an actual physical model obeying the desired theoretical equations. Since the quantities involved can be evaluated only by measurement, the attainable precision is necessarily limited. The slide-rule is a familiar example of an analogue computer, using lengths to represent the logarithms of numbers.
Digital computers operate upon numbers in some coded-digit form and make use of standard computational techniques to obtain direct numerical solutions to problems. By increasing the number of digits with which numbers are represented in the machine, the precision may be extended without limit. A desk calculator is a simple form of digital computer.
1.2.1 Digital Computers
As a more complete form of digital computer, we may consider the combination of a desk calculator and its operator as a single computing unit; this will enable us to introduce the essential features of a typical digital computer:-
- Input and Output. This is one of the roles performed by the operator of a desk calculator, who must set up numbers in the machine before they can be operated on and also read results from the machine, recording them elsewhere. For an electronic computer, information is transferred to and from the machine by automatic equipment.
- Contro1. Here again, it is the operator who must control the sequence of operations on a desk calculator. An automatic computer is controlled by a program consisting of a sequence of detailed instructions in coded form. In the important case of a stored-program computer, the whole program is stored within the machine before any of it is obeyed; the speed of the computation is then not restricted to that of the input devices.
- Arithmetic Unit. The mechanism of a desk calculator carries out the individual operations in accordance with the key depressed. Similarly, the arithmetic unit of an electronic computer performs the functions called for by the successive instructions in the program. There will usually be included an accumulator in which the result of each step first appears, similar to the long register on the carriage of a desk machine.
- Storage. The keyboard and certain other registers of a desk calculator constitute a working store, insofar as the mechanism of the arithmetic unit is able to operate directly upon numbers contained in these registers. An electronic computer commonly has a working store capable of holding several thousand numbers. At any time each of these numbers is immediately available to the arithmetic unit, and so one speaks of a random access or fast store.
This type of storage is relatively expensive and so if still larger amounts of storage are required this is normally provided by some cheaper form of backing store. This will inevitably involve a longer access time, but, when required for computation, data can be transferred in blocks of several hundred numbers at once from the backing store to working store.
Each of the locations in the backing store and in the computing store is assigned an address. The address is a number, and it is important to distinguish the number which is the address of a location from the number which is contained in that location. As a means of distinction, we shall denote addresses by capital letters and contents by small letters and will assume, for example, that the number s is the content of the location whose address is S. In certain contexts we shall find it necessary to use the notation C(S) as an alternative to s. (Note that C(S+1) is not the same as s+1; the notation S* is sometimes used to denote S + 1, so that s* = C(S + 1). The contents of S after an operation will be written s', so that, for example, the equation
s' = s + b
denotes the operation of adding the number b to the contents of S.
1.4 Instruction Code
We have so far spoken of the contents of store locations as numbers but they may also be instructions in coded form. Both numbers and coded instructions may be referred to as words; it is for the programmer to ensure that no attempt is made to interpret one type of word as the other. An instruction word will usually contain one or more addresses to specify the data to be operated on; there will also be a coded number specifying the operation to be performed. The correspondence between the elementary operations which may be directly carried out in the arithmetic unit and the code numbers which control them constitutes the order-code or instruction-code of the computer.
1.5 Jump Instructions
Instructions will generally be obeyed in the same sequential order as their addresses occur in the store. However, it is possible to specify by an instruction the address of the next instruction to be obeyed, and hence one may arrange to jump out of sequence to an instruction at any desired address. Instructions are provided to make such a jump conditional upon the sign of certain numbers in the machine; these conditional jumps provide the ability to take elementary decisions.
By repeatedly jumping back to the same instruction, the computer can be made to obey a loop of instructions over and over again; this is a vital feature of high-speed computing, making it possible for a program of reasonable length to control the machine for relatively long periods of time.
The utility of computing loops is greatly enhanced by the facility known as modification, whereby different data is processed in each iteration of the loop. The store address of the number to be operated on is modified before use by the addition of an index stored in one of several special registers. Thus, if the index is increased by unity before each successive iteration, one may operate upon a list of numbers held in the store, and so, for example, form their sum or average.
1.6 Binary Numbers
The storage mechanisms used in electronic digital computers are normally made up of devices having two possible states, just as a switch may be either OFF or ON. If we associate with these two states the symbols 0 and 1 respectively, we are led to adopt the binary number system: the string of 0 's and l's stored on a row of two-state devices is interpreted as a succession of coefficients of powers of two in a polynomial. This is exactly analogous to the conventional decimal notation based on powers of ten. The binary digits 0 and 1 are commonly referred to as bits.
1.6.1 Negative Numbers
If a desk calculator is used to subtract some small numbers from zero, the result is characterised by a string of 9's at the more-significant end; the same operation with binary numbers produces a string of l's. We have here a naturally occurring representation of negative numbers, which is made unambiguous by restricting the range of positive numbers to those having 0 as their most-significant digit. This then becomes a sign digit, and the presence of a 1 in this position will indicate a negative number whose actual value is obtainable by subtracting 2r, r being the number of bits in the number.