After studying this section you should be able to do the following.

• Recognise and use the terminology: disjoint union; power set (of a set); representation (of a data abstraction).

• Use and interpret the notation:

Â

• X
Author(s): The Open University

In Section 2, we introduced the notation SeqOfX for the set of all sequences whose members come from the set X. In Section 2, we looked only at sequences whose members were of one of the primitive forms of data (integers, characters or Booleans). We can have sequences whose members are themselves data with a more complicated form. For example, suppose that Jo is working at the till T1 and is replaced by Jessica. We might represent this handover by the 3-tuple (Jo, T1, Jes
Author(s): The Open University

## The T822 course team

David Reed (Chair and author)

Jill Alger (Editor)

Chris Bissell (Critical reader and author)

David Chapman (Author)

Glen Darby (Graphic designer)

Donna Deacon (Course secretary)

Alan Dolan (Course manager)

Roger Jones (Author)

Jo Lambert (Learning projects manager)

Roy Lawrance (Gra
Author(s): The Open University

The primary functions of the ATM layer are associated with the routing and switching of ATM cells. Because ATM cells are packets, the switches are packet switches and the switching operation can be called forwarding, but by convention, because the ATM layer provides a connection-oriented service, the term â€˜forwardingâ€™ is generally not used.

The path cells take and the resources allocated to them depend on their service category. This is determined when a virtual connection is
Author(s): The Open University

The ATM physical layer is divided into two sub-layers: the transmission convergence sub-layer and the physical medium sub-layer.

Functions of the transmission convergence sub-layer include generating and receiving cells, and generating and verifying the cyclic redundancy check in the header error control field. For correct interpretation of ATM cells it is important to identify the beginning of a cell. In theory, if ATM cells are transmitted as a continuous stream of bits,
Author(s): The Open University

At the time of writing (2002), two versions of IP are available: versions 4 and 6. In this section I shall describe version 4, which is abbreviated to IPv4, as it is the more widely available version. Version 6 may eventually replace version 4 because it has some additional features that may prove essential for multiservice networks.

IPv4 is the main TCP/IP protocol in the internetwork layer of the TCP/IP reference model. It supports a connectionless service between hosts in an interne
Author(s): The Open University

In this section, I shall look at one example of an application of the TCP/IP protocol suite â€“ sending hypertext pages over the world wide web (WWW or simply the web). However, first I shall very briefly summarise the main features of the web that are relevant to this discussion. There are many sources of information about the web on the web itself for those who want to know more.

In very basic terms, the web is an application of the Internet for accessing resources where
Author(s): The Open University

The Internet is a worldwide public internetwork, which allows computers to communicate with each other even though they may have different manufacturers and different operating systems. The origins of the Internet lie in a project of the US Defense Advanced Research Project Agency in the 1970s, where it was intended to foster communication between research institutions rather than operate for profit. However, a substantial amount of traffic carried by the Internet is now related to com
Author(s): The Open University

There are several functions that can be performed at one or more of the OSI layers. Some of the more common ones are discussed below.

Connection control

For connection-oriented services, a connection must be established between peer entities. A connection has three phases: connection set-up, data transfer and connection clear. If the peer protocol supports connections, each protocol data unit type corresponds to a primitive type; for instance, a connection request primiti
Author(s): The Open University

In the OSI reference model there is a clear separation of services and protocols, but this separation is not always evident in practical applications, so it is worthwhile spending some more time on the differences between them. A service is provided by one layer to the layer above, and the capabilities of a service are defined in terms of primitives and their parameters. A service relates to two adjacent layers in the same system. In contrast, a protocol defines the communication between two
Author(s): The Open University

An internetwork is a network of networks, composed of terminals, switches and communication media. The overall objective of an internetwork is to allow communication between two (or more) networks. This simple description hides the complications that arise in real networks, in which the types of medium vary, transmission errors occur, transmission links fail, switches fail or become congested, equipment is produced by different manufacturers, networks are owned and maintained by differ
Author(s): The Open University

Early automatic telephone networks were built to carry only voice traffic and to provide a very simple telephone service â€“ now called plain old telephone service (POTS). When computer networks started to appear, either they were separate from telephone networks or the data carried between computers was a small proportion of the traffic on the telephone network. There are various estimates for the growth of voice and data traffic, and various dates have been given for when data traffic will
Author(s): The Open University

People have always communicated with each other â€“ initially by face-to-face communication through gestures and sounds, then over a distance through written messages and signals in the form of fires, lights or flags. Technology, for instance in the form of electrical signals, has reduced many of the limitations of distance. Communication networks have become very important, and modern society depends on them for the smooth operation of economic and social activities. In this unit we regard a
Author(s): The Open University

In this section I've briefly considered the very contentious question of what digital representations mean, but this debate must be left to another course. I have also described some of the devices that take digital information back into the analogue world of sight and sound, presenting it in a form that is meaningful to human eyes and ears.

Author(s): The Open University

Colour models were dealt with in Subsection 4.7.

You probably also own a printer. Many computers now come with them as part of a package. There are two main types in use today: inkjets and lasers.

InkJet printers work, as their name suggests, by firing tiny droplets of ink at the p
Author(s): The Open University

Every computer comes with a keyboard. They are still the main way of taking text across the boundary into the computer. The one I'm using to type this unit has 109 keys. Under each key is a pressure sensor that detects when the key has been pressed and sends an electronic signal into the computer. There, a small program called the BIOS (Basic Input/Output System) translates the signal into the appropriate numeric code. Other software stores that code in a suitable place in the memory.

Author(s): The Open University

They are neither finite quantities, or quantities infinitely small, nor yet nothing. May we not call them the ghosts of departed quantities?

(Bishop G. Berkeley, The Analyst)

This section follows up the ideas presented in and aims to:

• define the terms analogue, discrete and digital;

• look briefly at the human perceptual system, whic
Author(s): The Open University

Suppose I take a digital photograph of myself for my website. Horrified by my wrinkled, baggy appearance, what can I do? Actually, with the right software I can do more or less anything I like: I can smooth out the wrinkles; I can restore the grey hair to its former splendour; I can even put in a background of books to give me a scholarly appearance. In fact, I can so improve the picture that if you met the real me you probably wouldn't recognise me.

â€˜Massagingâ€™ my photographic imag
Author(s): The Open University

All materials included in this unit are derived from content originated at the Open University.

Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

1. Join the 200,000 students cur
Author(s): The Open University

The AND operation combines two binary words bit by bit according to the rules

• 0 AND 0 = 0

• 0 AND 1 = 0

• 1 AND 0 = 0

• 1 AND 1 = 1

In other words, only when both bits are 1 is the result 1. You may find it helpful to think of it this way: when one bit is one and the other bit is 1 the result is 1.

Author(s): The Open University