Information Technology Reference
In-Depth Information
In this system, 00000000 represents the decimal number 0;
00000001 represents the decimal number 1; 00000010 represents
the decimal number 2; and so forth. Following this pattern, the
largest number would be 11111111 or 128 + 64 + . . . + 2 + 1 or
255. Altogether, this approach allows us to store the integers 0
through 255, inclusive, for an 8bit number or byte, and we can
conclude that one byte of data can take on 256 different values. Of
course, this range is adequate for some data storage purposes in
computers, but not for others. The 8bit number with a range of
256 alternatives will arise several times later in this chapter and
throughout the topic.
represented inside computers?
At a very simple mechanical level, we can easily conclude that,
of course, there are limits on the size of numbers that machines can
store! Because the main memory of any computer is finite, a com
puter has storage limitations. We cannot store numbers of un
bounded size (e.g., integers with arbitrarily large numbers of digits)
in a finite space.
How, then, can we describe the limits we have on the numbers
we can store? Unfortunately, although this question is easy to ask,
the answer is fairly complex. There are two main approaches to
data storage:
1.
Fixedsizestorage approach:
Computers allocate a specified
amount of space for a number; the maximum size of an in
teger or a real number is predetermined by the computer's
circuitry.
2.
Variablesizestorage approach:
Space is allocated to numbers
as needed; small integers take up rather little space, whereas
very large integers require much more space.
Fixedsize Storage Approach: In the fixedsize storage approach,
a standard format and storage size are used for all integers or for real
numbers. (More about this format shortly.) Typically, the predeter
mined format and size can accommodate the data for common ap
plications, and the hardware circuitry in fixedpoint storage systems
