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## Number Systems and Number Representations

### Design of Digital Computers (1967-01-01): 5-22 , January 01, 1967

The familiar decimal system is by no means the only possible number system. Considered impartially, it merely constitutes one among possible and practical systems which became propagated, probably for the sole reason that human beings happen to have ten fingers. The Mayas used the vigesimal number system (based upon 20, i.e. fingers and toes) [1] and even in our days, there are some endeavors to introduce the duodecimal system (based on 12) for general use [2]. Since computers are not bound by tradition and since the decimal system has no unique merits, the designer of a computer is free to select that number system which suits his purpose best.

## A fixed-point theorem

### Mathematical systems theory (1967-03-01) 1: 55-57 , March 01, 1967

## Einführung in die allgemeine Informationstheorie

### Einführung in die allgemeine Informationstheorie (1967-01-01): 6 , January 01, 1967

## Der Satz von Feinstein

### Einführung in die Informationstheorie (1967-01-01): 17-22 , January 01, 1967

Feinstein hat 1954 in seiner sehr bekannt gewordenen Dissertation (vgl. [4]) den im folgenden genau behandelten Fundamentalsatz für Kanäle aufgestellt, der von großer Bedeutung für die Informationstheorie ist, weil er ohne Voraussetzungen über die speisenden Quellen allein aus den Eigenschaften des Übertragungskanals sehr weitreichende Aussagen liefert.

## Storage Elements

### Design of Digital Computers (1967-01-01): 78-103 , January 01, 1967

Logic elements alone—used in the straightforward manner shown in the previous chapter—are not sufficient to build a computer. It is necessary to have elements which perform the function of storage. This fundamental need can be illustrated by a basically simple example. Push-buttons with momentary contacts produce a certain output (opened or closed contacts) only as long as certain input conditions prevail (the button is pushed or not pushed). In this respect, they act like (and really are) logic elements. Using only such push-buttons, it will not be possible to design a circuit which turns a light on when a button is pressed, but leaves it on after the button is released. In order to accomplish this task, some storage element has to be incorporated into the circuit which stores (or “remembers”) the fact that the button had been pressed. The storage element may be a relay as in a push-button motor control, or a simple mechanical device, as in a toggle switch which keeps the switch in the position into which it had been set last.

## Invariance for ordinary differential equations

### Mathematical systems theory (1967-12-01) 1: 353-372 , December 01, 1967

## Einleitung

### Einführung in die allgemeine Informationstheorie (1967-01-01) 6: 1-4 , January 01, 1967

### Zusammenfassung

Die erste technische Anwendung des elektrischen Stromes war nach seiner Entdeckung die Fernübertragung von Nachrichten. Der Telegraph und das Telephon sind wesentlich älter als die Glühlampe oder der Elektromotor.

## Erratum to: Einleitung

### Einführung in die Informationstheorie (1967-01-01) : 30 , January 01, 1967

## The Functional Units of a Digital Computer

### Design of Digital Computers (1967-01-01): 179-366 , January 01, 1967

In chapter 7, the function of the arithmetic unit has been defined loosely as the performance of arithmetic operations. As such, the capabilities of the arithmetic unit have been compared to those of a desk calculator. Although this analogy is valid in a general sense, the capabilities of arithmetic units exceed those of the desk calculator: in addition to arithmetic operations, certain logic data manipulations can be performed. Moreover, the particular manner in which operations are performed is influenced by the electronic design. In the following paragraphs we shall discuss three types of operations: fixed-point arithmetic operations, logic operations, and floating-point arithmetic operations. Incidental to this discussion, we shall see structures required for the implementation of the individual operations. In conclusion, several sample layouts of arithmetic units are indicated in which the individual requirements are combined.

## Congruence separation of subsets of a monoid with applications to automata

### Mathematical systems theory (1967-12-01) 1: 315-324 , December 01, 1967

Let*F* be a monoid and let*A*={*A*_{i}*i*∈*I*} be a set of disjoint subsets of*F*, where*I* is an index set. A congruence on*F* is called*A*-separating if each of its congruence classes has a non-empty intersection with at most one A_{i} ∈*A* The set*C*_{′}^{A}
of all*A*-separating congruences on*F* is a lower semi-lattice with respect to the partial ordering of congruence inclusion. A necessary and sufficient condition for*C*_{′}^{A}
to be a complete lattice is derived and, in that case, the unique maximal*A*-separating congruence is characterized. The relation of*A*-separating congruences with automata is described. An example of the case that the unique maximal*A*-separating congruence on a free monoid exists is worked out, and its realization by an incompletely specified finite automaton is given.