Digital & Computing

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Crossing the boundary: analogue universe, digital worlds

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# 4.5 Resolution

## SAQ 10

What do you think could be done to improve the quality of the image?

One obvious way is to increase the number of squares and to make each square smaller.

Suppose we double the number of the gridlines in each direction, making each pixel one quarter the size of the ones in Figure 13. This is called increasing the resolution of the picture. The new grid is shown in Figure 15.

Figure 15 A higher resolution grid

Now if I again map each square to a black or white pixel, I get the image shown in Figure 16.

Figure 16 The image using a higher resolution grid

This is still a bit ragged, but an improvement. It's easy to see that if we go on and on increasing the resolution of the picture, making the pixel size smaller and smaller, we will move closer and closer to an image that appears completely smooth. But note that we can never reach a perfectly smooth image by this process – to do this one would need infinitely small pixels. We can never reach an analogue representation by digital means, only approximate to it.

## Exercise 10

Work out how many bits would be needed to store the image in Figure 16. How many bytes?

### Discussion

The image is 62 pixels wide by 44 pixels high, so we need 2728 bits to store it. As you will remember, there are 8 bits in a byte, so we will need 341 bytes to store this very simple image.

I will return to the issue of storage size later. But at the moment there is still a lot missing. This bitmap approach may be all right for simple images consisting of a few lines and some filled areas, but it will not be adequate for anything rather more subtle, such as the (still fairly modest) little pictures in Figure 17.

Figure 17 More sophisticated pictures

## SAQ 11

Why is the simple strategy used above not satisfactory for the pictures in Figure 17?

The most obvious point is that we have as yet no way of handling colour. Slightly less obvious, but just as important, is that plain black and white won't allow us to represent subtleties of light and shade shown on the picture of the aircraft.

The second point is somewhat more complex, so I will deal with it first. Any image tries to capture some aspect of the visual world. A glance back at the Vermeer painting reminds us of the analogue quality of light. There are no clear boundaries: between areas of brightness and darkness there are countless subtle textures of grey; boundaries are blurred by light and shadow. Our simple bitmap above is obviously too limited to handle such subtlety – it just deals in black and white. But there is no need to discard the basic idea. Can we adapt the simple bitmap strategy to deal with shade and texture?

Of course we can – and quite easily. In our previous example, we dedicated one bit to each pixel in our image. All we need to do is devote more bits to each pixel to accommodate a greater range of shades. Let's allocate two bits per pixel with binary 11 representing black and binary 00 standing for white.

## SAQ 12

How many shades can we represent using two bits per pixel? Remember your binary!