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1 At the supermarket

1.1 Number sequences

Imagine that you are at a modern supermarket and the cashier is processing the items from your basket or trolley. The electronic till (which is a form of computer) records each item that you have bought. Most items are scanned using a device that can read the barcode printed on the item.

View larger image

Figure 1: An example of a barcode. Today, nearly every product has a barcode, although not all stores use them. A laser scanner is used to convert the pattern of light and dark bars into a number stored in the till. The number, printed as part of the barcode, may be entered manually if an electronic scanner is unavailable. A computerised till uses this code to look up the price that a shop wishes to charge for the item.

Items that need to be weighed (such as loose fruit and vegetables) do not have a barcode printed on them. Instead, the cashier looks up a different sort of code for these items and enters this manually at the till, together with the weight of the item purchased. If an error is made, the cashier may cancel the item just entered and try again. When all the items you have purchased have been processed, your final bill is calculated and you receive an itemised receipt (Figure 2).

Figure 2: An example of a supermarket till receipt. (Note the two weighed items.)

Let us look a little more formally at some of the data that the supermarket computer system must store and use. As we do this, you will begin to get a flavour of the rigour that underpins the design of modern software. You will meet new vocabulary and concepts, try to get a general sense of what each new term means.

Each type of item stocked by the supermarket needs to be identified. As we have seen, this is done either using barcodes or, for weighed items, item codes of a different sort. Associated with each code is a variety of other item-related information. Perhaps the most obvious information is the price, and the description that appears on the receipt. (In the case of weighed items, the price is a unit price, giving the price per kilogram, for instance.) Other information associated with any item code might include the current stock level (so that new stock can be ordered as items are near to being out of stock), the name and address of the supplier, discount rates for multiple purchases, etc.

Barcodes such as 5000119004048 can be interpreted as whole numbers. Whole numbers are called integers. Integers may be positive, negative or zero. (The codes for weighed items are also usually whole numbers.)

Prices and weights are not ordinarily presented as whole numbers. In Figure 2, the item price of walnut bread is shown as £1.49; the unit price of organic courgettes is £3.49 per kg and the weight of organic courgettes purchased is 0.41 kg (kg is the standard abbreviation for kilogram).

A number with a fractional part such as 1.49 is an example of a real number. The real numbers include numbers such as 3.497825 (and numbers such as √2, which cannot be expressed exactly as any fraction or decimal). Computers cannot represent such real numbers exactly. When dealing with a real number, we can only rely on a computer storing and manipulating an approximation of the number. Even though the extent of the approximation may seem small, this can present problems to the unwary software developer. To avoid problems here, we will represent prices as a whole number of pence, and weights as a whole number of grams.

1.1 Number sequences

Imagine that you are at a modern supermarket and the cashier is processing the items from your basket or trolley. The electronic till (which is a form of computer) records each item that you have bought. Most items are scanned using a device that can read the barcode printed on the item.

View larger image

Figure 1: An example of a barcode. Today, nearly every product has a barcode, although not all stores use them. A laser scanner is used to convert the pattern of light and dark bars into a number stored in the till. The number, printed as part of the barcode, may be entered manually if an electronic scanner is unavailable. A computerised till uses this code to look up the price that a shop wishes to charge for the item.

Items that need to be weighed (such as loose fruit and vegetables) do not have a barcode printed on them. Instead, the cashier looks up a different sort of code for these items and enters this manually at the till, together with the weight of the item purchased. If an error is made, the cashier may cancel the item just entered and try again. When all the items you have purchased have been processed, your final bill is calculated and you receive an itemised receipt (Figure 2).

Figure 2: An example of a supermarket till receipt. (Note the two weighed items.)

Let us look a little more formally at some of the data that the supermarket computer system must store and use. As we do this, you will begin to get a flavour of the rigour that underpins the design of modern software. You will meet new vocabulary and concepts, try to get a general sense of what each new term means.

Each type of item stocked by the supermarket needs to be identified. As we have seen, this is done either using barcodes or, for weighed items, item codes of a different sort. Associated with each code is a variety of other item-related information. Perhaps the most obvious information is the price, and the description that appears on the receipt. (In the case of weighed items, the price is a unit price, giving the price per kilogram, for instance.) Other information associated with any item code might include the current stock level (so that new stock can be ordered as items are near to being out of stock), the name and address of the supplier, discount rates for multiple purchases, etc.

Barcodes such as 5000119004048 can be interpreted as whole numbers. Whole numbers are called integers. Integers may be positive, negative or zero. (The codes for weighed items are also usually whole numbers.)

Prices and weights are not ordinarily presented as whole numbers. In Figure 2, the item price of walnut bread is shown as £1.49; the unit price of organic courgettes is £3.49 per kg and the weight of organic courgettes purchased is 0.41 kg (kg is the standard abbreviation for kilogram).

A number with a fractional part such as 1.49 is an example of a real number. The real numbers include numbers such as 3.497825 (and numbers such as √2, which cannot be expressed exactly as any fraction or decimal). Computers cannot represent such real numbers exactly. When dealing with a real number, we can only rely on a computer storing and manipulating an approximation of the number. Even though the extent of the approximation may seem small, this can present problems to the unwary software developer. To avoid problems here, we will represent prices as a whole number of pence, and weights as a whole number of grams.

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