A function is a process that, when given an input of a specified type, yields a unique output. This is a key idea in providing a precise, mathematical, description of processes in computing.
To describe a particular function, we first give the set from which the input will be drawn and the set from which the output is drawn. This information is called the signature of the function. An example will make this clearer. Author(s):
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:

X

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 3tuple (Jo, T1, Jes
The T822 course team
David Reed (Chair and author)
Jill Alger (Editor)
Chris Bissell (Critical reader and author)
Philippa Broadbent (Print buyer)
David Chapman (Author)
Daphne Cross (Assistant print buyer)
Glen Darby (Graphic designer)
Donna Deacon (Course secretary)
Alan Dolan (Course manager)
Roger Jones (Author)
Jo Lambert (Learning projects manager)
Roy Lawrance (Gra
3.3 Hypertext transfer protocol (HTTP)
In this section, I shall look at one example of an application of the TCP/IP protocol suite – 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
3.1 What does TCP/IP protocol architecture do?
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
2.4 Examples of layer functions
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 connectionoriented services, a connection must be established between peer entities. A connection has three phases: connection setup, 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
1.2 Protocols in multiservice networks: introduction
Early automatic telephone networks were built to carry only voice traffic and to provide a very simple telephone service – 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
3.1 Ghosts of departed quantities
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
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.
‘Massaging’ my photographic imag
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.
7.4 Multiplying 2's complement integers
Multiplication can be thought of as repeated addition. For instance, in denary arithmetic
7 × 5
can be thought of as
7 + 7 + 7 + 7 + 7
There is therefore no need for a new process for the multiplication of binary integers; multiplication can be transformed into repeated addition.
In multiplication the result is very often much larger than either of the two integers being multiplied, and so a multiplelength representation may be needed to hold the result of a mu
2.2.3 Positive integers: converting denary numbers to binary
If computers encode the denary numbers of the everyday world as binary numbers, then clearly there needs to be conversion from denary to binary and vice versa. You have just seen how to convert binary numbers to denary, because I did a couple of examples to show you how binary numbers ‘work’. But how can denary numbers be converted to binary? I'll show you by means of an example.
2.2.2 Positive integers: binary numbers
Just as a denary number system uses ten different digits (0, 1, 2, 3, … 9), a binary number system uses two (0, 1).
Once again the idea of positional notation is important. You have just seen that the weightings which apply to the digits in a denary number are the exponents of ten. With binary numbers, where only two digits are used, the weightings applied to the digits are exponents of two.
The rightmost bit is given the weighting of 2°, which is 1. The ne
Generally, when we talk about communication between humans, we mean one person conveying information to another person. Figure 6 shows a basic model, or representation, of a communication system for getting a message from the sender to the recipient. The diagram shows the sender (User
This unit is from our archive and it is an adapted extract from Networked living: exploring information and communication technologies (T175) which is no longer in presentation. If you wish to study formally at The Open University, you may wish to explore the courses we offer in this curriculum area.
This unit will introduce you to some ideas about how information and
Reverting to the relational database we constructed in Section 3.3, you might wonder what, from the user's point of view, has been gained by creating separate tables for the students and courses. With Table 1 you could see at a glance who was studying what. In the relational database it was har
All the data we have had so far in the database has been text or numbers. I have mentioned that another type of data might be dates. Modern databases, however, can store other kinds of data than text, numbers and dates. They can also store graphics, moving pictures and sounds.
Activity 12 (exploratory)
In many countries, egovernment has become part of government policy. The UK government has a large egovernment project under way, as do the governments of the USA, Australia and Japan, to name just a few. The ‘e’ at the start of ‘egovernment’ stands for ‘electronic’, and egovernment usually refers to the use by governments of ICTs. In many ways egovernment is not a single activity but many activities. However, in the UK and many other countries, there is a degree of central c
1.6.2 Different types of sound
Sounds come in four categories.

Sound effects. Many UIs contain a range of warning beeps and reassuring sounds confirming that operations have been completed. These can include naturalistic sounds, such as the sound of a piece of screwedup paper dropping into a waste paper basket.

Music. Many composers use computer systems to compose music, and programs such as games make extensive use of music. Short sequences of mus