Motorola M68000 Betriebsanweisung PDF herunterladen (Seite 19)

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NUMBER SYSTEMS

Throughout history mankind has used a variety of methods to rep

resent numerical quantities. Early man used piles of stones, each stone

representing one unit of those items being counted. It soon became ob

vious that for large numbers, a large number of stones were required.

One solution to this problem was to use stones of different sizes. A sin

gle large stone could be used to represent a pile of smaller stones. This is

similar to the use of the denominations of paper currency. Schemes like

this work well for physical entities like coins or stones. However, to rep

resent quantities on paper we would be forced to draw pictures of our

piles of stones.

Decimal

Our decimal number system is a product of all these schemes. Instead

of piles of different numbers of stones or stones of different sizes, the

Arabic numerals 0 to 9 and the relative position of these numerals are

used to represent the number of stones in a pile and the relative size

of the stones. The numerals 0 to 9 can represent quantities from zero to

nine. Position can be used to represent any number of sizes. For example,

the decimal number “23” can be thought of as representing three small

stones and two larger stones. If each larger stone is equivalent to ten

small stones, this number represents the equivalent of twenty-three small

stones. This may seem obvious to most readers, but it is the basis of all

the number systems we will study.

In the decimal number system, each digit’s position represents a dif

ferent power of 10. For example, the number 7458 is equivalent to:

7(10)3+4(10)2+5(10)1+8(10)°

The choice of 10 as the numerical base, or radix, as it is sometimes called,

is arbitrary. We can create a number system using any base we desire.

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Motorola M68000 Betriebsanweisung Seite 19