Primitive data types expanded
Introduction
When a computer stores data in a program or an application such as a database, it needs to know what type of data it is. This is because different data types require different amounts of storage space. Before we look at storing data in both fixed-size records and variable-sized records, we need to look in a little more detail at the most common data types. Some data types can be found in most programming languages. Some data types may be found in applications such as Access.
Integers
An integer is a positive or negative whole number. It has no fractional part. 5, -23 and 800 are examples of integers while 5.7,
-23.98 and 4.0 are all real numbers because they have a fractional part (even if the fractional part equals zero).
We have already seen some methods of storing integers. We have seen the pure binary method of representing integers, the sign and magnitude system and the two's complement system. Using the pure binary method, for example, we can represent whole positive numbers between 0 and 255 if we use one byte. That's because there are 256 unique combinations of 8 bits. (0000 0000, 0000 0001, 0000 0010, 0000 0011, up to 1111 1111). One byte per integer is of little use, however, if you need to store numbers between 0 and 1000, for example. In this case, two bytes would be needed. If we use two bytes, we can represent integers between 0 and 65535.
We know that pure binary is of no use if we want to represent negative numbers. In this case, we could use sign and magnitude if we just want to hold a positive or negative number but don't need to do any calculations on the numbers. If calculations on positive or negative numbers are needed, then the two's complement system should be selected. The key questions to ask, then, when deciding on what binary system to use to represent integers are:
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- What range of numbers do I need to store?
- Do I need to hold negative as well as positive numbers?
- Do I need to do calculations on the numbers?
Real numbers
Real numbers are numbers that have a fractional part. For example 6.7 and -23.65 are real numbers because they both have a fractional part. So far, we have only looked at using a byte or two bytes to represent integers. To represent real numbers in a computer, we use a system called the ‘floating-point’ system. How is this used to store a real number?
Consider this. The number 3547.54 is a real number. It’s quite complex in that it has a whole part and a fractional part. This number can also be represented as 0.354754 x 104. The 0.354754 is known as the ‘mantissa’ and the 4 is known as the ‘exponent’. If I now store both the mantissa and the exponent, I can store all the information I need to get back to the original number. You may have come across this way of representing numbers before in your maths lessons. It’s known as ‘standard form’. If you want to represent a real number then, you need to store both the mantissa and the exponent. If you only used one byte, the range and the accuracy of the numbers you could store would be very limited. Real numbers are therefore usually represented using either 2 bytes or 4 bytes. We will look in much more detail at floating-point numbers and become expert in their use later in the book!
String
Data type string is used to hold a string of any characters (letters, numbers, special characters or control characters) from the keyboard. We have already seen that PCs use ASCII. Every character on the keyboard has a unique binary code. To represent each character requires 1 byte. If you were setting up a database, for example, and you needed to store the NAME of someone, you would define NAME to be a data type ‘text’ because each name is made up of a string of characters from the keyboard. But how many characters should you allow? You need to think what the longest name possible is and then add a bit, just in case! For example, you might decide the longest name you can think of is 20 characters long. You need to allow 20 bytes of storage space for every person's name, plus say an extra 5 for 'insurance' - just in case there is a slightly longer name than you thought of! The amount of storage space will quickly increase as the number of NAMEs you store increases. There is a trick you can use, however, to reduce the amount of space you need.
Coding text values to save on storage space
Suppose you had a university database that stored each NAME OF STUDENT at university and the TITLE OF DEGREE they were doing. There are 100 different degrees. If you had allowed 100 bytes for each TITLE OF DEGREE and you had 10 000 students, you would need 1 000 000 bytes to store their degrees. However, if we coded up the titles of degrees (Maths could be code MA, History of Art could be HA and so on) then we would only need to store two bytes per student for the title of degree. This method of coding is a very useful way of reducing the amount of storage space needed so long as there are a fixed number of choices. It enables you to store lots of pieces of information as a short code. It wouldn't be a suitable method for NAME OF STUDENT, for example, because there are an endless number of possible names!
There are some other benefits of coding data. It helps reduce the amount of time needed to enter in a particular piece of data into a database. If the codes are selected in a certain way, only authorised people will know what they mean. Therefore the data is slightly more secure. In addition, you can easily apply validation rules to codes whereas applying them to long text values is difficult.
Character
Data type ‘character’ is used to store just one character from the keyboard. It is usually a letter that is stored. For example, you might have in a university database the LOCATION of a degree, what campus it is taught on. You might have a choice of four locations, which have been coded up into A, B, C or D. However, any character, whether text, number, special or control, can be stored in this data type.
Boolean
Any piece of information that can have two and only two choices should be declared as data type Boolean. For example, GENDER should be Boolean because there are only two choices. ‘UK STUDENT?’ should be data type Boolean because every student is either a UK student, or not. Each Boolean data item needs one bit to hold its value. For example, 'bit three' could be set if the gender of the student is male and reset if they are female. One byte can be used to hold 8 Boolean data items.
Date
Date fields hold calendar dates! You need to decide, however, what format you want the date to be in because this affects how many bytes you need to store the date. For example, if you want the date to be DD/MM/YY (for example, 21/08/86) then you need 6 bytes. (You don't need to store the / symbol between the numbers). If, however, you want the date in the form DD/MM/YYYY (for example, 21/08/1986) then you need 8 bytes.
Calculated fields
It is worth mentioning that some pieces of data aren't stored at all and so may not need to be declared in the same way as pieces of data that are stored. For example, calculated fields are used in databases. These pieces of information are not stored in a database or a program, but are calculated at the time they are needed from pieces of information that you have stored!
You can show how clever you are in any database project by using a calculated field. A classic example is where you store someone's DATE_OF_BIRTH (data type DATE, 6 or 8 bytes) but you don't store their age. (If you did store their age rather than their date of birth, you would have to change each record every single year!!) If you needed to display someone's age, perhaps in a report, then you would calculate it in the background with programming code, using their DATE_OF_BIRTH information and the computer’s internal date. The code to do this for any programming language you are familiar with can be found by searching the Internet.
Telephone numbers and other non-integer codes
Just because a number is made up of numbers doesn't mean it is a number!! A telephone number, for example, isn't a number in the sense that it's an amount of something. You can't add a telephone number to another telephone number to get a sum of telephone numbers! A telephone number is better described as a code. A number should only be declared a data type number if you may need to do calculations with it. If you don't ever need to do calculations with it then it is safer to declare it as text (or as a BCD, Binary Coded Decimal) number. This is because leading zeros in integers are removed but are not removed if the piece of data is a data type text or BCD! Try, for example, typing in 00243 into a calculator. Either it won’t enter the leading zeros or it removes them after you have entered the number in. Telephone numbers sometimes begin with a leading zero and so should be declared as data type text or BCD. If you had a phone number 764880, you could use 6 bytes if the data type was declared as a text. One byte would be used to represent the 7. The second byte would be used to represent the 6, and so on. You could, however, use 3 bytes to store the number as a BCD number in the following way:
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- You would store 0111 0110 in the first byte. (The 7 would occupy the 4 bits on the left of the first byte and the 6 would occupy the 4 bits on the right of the first byte.
- You would store 0100 1000 in the second byte. (The 4 would occupy the 4 bits on the left of this byte and the 8 would occupy the 4 bits on the right of this byte).
- You would store 1000 0000 in the second byte. (The 8 would occupy the 4 bits on the left of this byte and the 0 would occupy the 4 bits on the right of this byte).
There are other examples of ‘numbers’ that are really codes - they are never 'added’, for example, to other ‘numbers’. Consider a 6-digit product code on an item of clothing in a shop that is made up only of numbers. The numbers in the code mean something - they are codes rather than numbers. For example, the first number might show a type of product, the next 2 numbers might be a 'country of origin' code and the last three numbers might be the manufacturer's ID. You may need to strip out these numbers from a code, and the first number might also be a zero. You will never need to add one code to another, however, because this type of calculation for this piece of data is a nonsense.