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4.2 Text

As I said in the human perceptual system is very strongly based on vision and hearing. When we think, we usually do so in terms of pictures and, perhaps to a lesser extent, spoken words and sounds. However, the simplest place to start thinking about how we can reduce human experience to numbers is with a very advanced human concept: written text.


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3.11 Summary

In this section I examined the terms analogue, discrete and digital and illustrated their correct use through examples and brief definitions.

I raised the familiar idea of the five human senses which enable us to perceive our analogue world.

Finally I focused on the digital world of counting and representing numbers, and in particular the binary system used in the inner world of the computer.


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3.8 How computers work with numbers

Today's mass media wrap computers in a damaging myth. The message of TV thrillers seems to be that computers are inscrutable, subtle devices, far beyond the ordinary person's comprehension. Only spectacularly gifted, young, ‘cool’ people seem to be capable of working with them successfully. For such individuals, a few clicks on the keyboard work miracles. The myth suggests that when we less gifted mortals use a computer and something goes wrong, it's our fault. We're simply too stupid for
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3.7 How we work with numbers

Most civilisations have had to face the problem of counting and recording numbers. Our own culture has adopted the so-called Arabic system of numbers. This system is now used more or less worldwide. In this section I will look very briefly at some of its key features.

We have an infinity of numbers at our disposal. If we start counting from 1, we can in theory go on for ever. But although there is an infinity of numbers, we only have a very small, fixed number of digits to
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3.5 Digital things

The terms ‘discrete’ and ‘digital’ are often used interchangeably. For example, The New Penguin Dictionary of Computing contains the following definition.

Digital. Any communication or computing technology whose data may only have a finite number of discrete values.

However, I want you to be clear about the strong association between a digital thing and a number
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2.8 The price

But using computers to acquire, store, exchange and manipulate data comes at a price. By this, I don't mean that the technology is expensive, although this may be an issue. Rather it's the fact that the quality of the information computers give us can often be suspect. More worrying still are the questions of privacy, liberty and security that are raised. The computer gives ordinary people unprecedented access to information. But it also gives people that might not wish us well – gov
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2.6 Going back

Capturing bits of reality and transferring them to a computer would be a pointless exercise if they stayed locked in the digital world. We want access to what we've captured. We want to see the results. In particular, we may want to look at our captive in a different form. For instance, suppose we input the series of temperature readings shown in Author(s): The Open University

2.5: Crossing the boundary

So computers are used to acquire, store and present, exchange, and manipulate interesting characteristics of the world. But this raises a serious problem: the world we inhabit and know so well and the world inside the computer are very different in kind. We live in an analogue world. The world of the computer is digital. The exact meaning of these terms may not be very clear to you at the moment. I will define them both in the next section. For the moment, the only point
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2.4.4 Manipulation

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
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2.4.3 Exchange

Being able to link computers into networks has enormously boosted their capabilities. Data can now be sent between any two computers, maybe thousands of miles apart, at the speed of light. For example, I can share the digital photo stored on my computer with people all over the world almost instantaneously, simply by sending the image to them as an email attachment. Or I can go further and post the image to a website on the internet, where it will be publicly available for any suitably equipp
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2.4 The pervasive computer

We can start with a simple proposition:

The computer's job is to acquire, store, present, control, exchange and manipulate interesting characteristics of the natural world.

So what are ‘interesting characteristics of the natural world‘? Obviously that depends on your point of view. An ordinary tourist might want to capture a memory of some scene she was experiencing – moonlight on the
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1 Aims

In this course, I want to be more specific and look at the way computers represent and handle data. The course aims to:

  • broaden the definition of a computer and explain the concept of crossing the boundary between the computer's world and our own

  • explain the digital nature of the computer's world and contrast it with our analogue world of sense and motion

  • describe in detail how to transform features of our world in
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Learning outcomes

After studying this course, you should be able to:

  • give examples of quantities that are intrinsically analogue, and quantities that are intrinsically discrete/digital

  • define the terms ‘bit’, ‘byte’ and ‘word’

  • outline how visual information, such as pictures, diagrams and moving images can be expressed numerically inside a computer

  • describe how sounds such as speech and music can be represented inside a computer in terms of
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Keep on learning

Study another free course

There are more than 800 courses on OpenLearn for you to
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8.6 Summary

The logic operations introduced here are summarised in Table 1, which is an example of what is known as a ‘truth table’. It shows what the result (‘output’) of each logic operation is for all possible combinations of ‘input’ values. You may find this format a useful one for remembering t
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8.5 The exclusive-OR operation

The exclusive-OR operation (usually abbreviated to XOR, pronounced ‘ex-or’) combines two binary words, bit by bit, according to the rules:

  • 0 XOR 0 = 0

  • 0 XOR 1 = 1

  • 1 XOR 0 = 1

  • 1 XOR 1 = 0

In other words, the result is 1 when either bit is 1 but not when both bits are 1 or both bits are 0, or the result is 1 when the two bits are different and 0 when they are the sam
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8.4 The OR operation

The OR operation (occasionally called the inclusive-OR operation to distinguish it more clearly from the exclusive-OR operation which I shall be introducing shortly) combines binary words bit by bit according to the rules:

  • 0 OR 0 = 0

  • 0 OR 1 = 1

  • 1 OR 0 = 1

  • 1 OR 1 = 1

In other words, the result is 1 when either bit is 1 or when both bits are 1; alternativel
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7.5 Dividing 2's complement integers

Just as multiplication can be turned into repeated additions, so division can be turned into repeated subtractions. And just as shifting a binary integer one place to the left equates to multiplying by two, so shifting a binary integer one place to the right equates to dividing by two.

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7.3.2 Subtraction

As I indicated at the start of this section, subtraction is converted to addition by replacing the number to be subtracted by its additive inverse, which in the case of binary arithmetic is its 2's complement. An example should make this clear.

Example 9

Subtract the signe
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4.4 Representing sound

Sound, such as speech or music, is an analogue physical quantity that varies with time, and so the ideas you have already met in Section 2.5 about converting analogue weights to digital form are relevant here too. In particular, samples of the sound will have to be taken, and each sample will have to be quantised to the nearest binary code in the digital representation.

It's important to appreciate that sound such as speech or music varies rapidly with time, and so samples of it will ha
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