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Ranges for each of the whole-number types
Figure 1 shows the range of values that can be accommodated by each of the four whole-number types supported by the Java programminglanguage:
| Figure 1 . Range of values for whole-number types. |
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byte
-128 to +127short
-32768 to +32767int
-2147483648 to +2147483647long
-9223372036854775808 to +9223372036854775807 |
Can represent some fairly large values
As you can see, the int and long types can represent some fairly large values. However, if your task involves calculations such as distances in interstellar space, these ranges probably won't accommodate your needs. This will lead you to consider using the floating-point types discussed in the upcoming sections. I will discuss the operations that can be performed on whole-number types more fully in futuremodules.
Floating-point types are a little more complicated than whole-number types. I found the definition of floating-point shown in Figure 2 in the Free On-Line Dictionary of Computing at this URL .
| Figure 2 . Definition of floating point. |
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A number representation consisting of a mantissa, M, an exponent, E, and an (assumed) radix (or "base") . The number represented is M*R^E where R is the radix - usually ten but sometimes 2. |
So what does this really mean?
Assuming a base or radix of 10, I will attempt to explain it using an example.
Consider the following value:
623.57185
I can represent this value in any of the ways shown in Figure 3 (where * indicates multiplication).
| Figure 3 . Different ways to represent 623.57185. |
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.62357185*1000
6.2357185*10062.357185*10
623.57185*16235.7185*0.1
62357.185*0.01623571.85*0.001
6235718.5*0.000162357185.*0.00001 |
In other words, I can represent the value as a mantissa (62357185) multiplied by a factor where the purpose of the factor is to represent a left or right shift in the position of the decimal point.
Now consider the factor
Each of the factors shown in Figure 3 represents the value of ten raised to some specific power, such as ten squared, ten cubed, ten raised to the fourth power, etc.
Exponentiation
If we allow the following symbol (^) to represent exponentiation (raising to a power) and allow the following symbol (/) to represent division, then we can write the values for the above factors in the ways shown in Figure 4 .
Note in particular the characters following the first equal character (=) on each line, which I will refer to later as the exponents.
| Figure 4 . Relationships between multiplicative factors and exponentiation. |
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1000 = 10^+3 = 1*10*10*10
100 = 10^+2 = 1*10*1010 = 10^+1 = 1*10
1 = 10^+0 = 10.1 = 10^-1 = 1/10
0.01 = 10^-2 = 1/(10*10)0.001 = 10^-3 = 1/(10*10*10)
0.0001 = 10^-4 = 1/(10*10*10*10)0.00001 = 10^-5 = 1/(10*10*10*10*10) |
In the above notation, the term 10^+3 means 10 raised to the third power.
The zeroth power
By definition, the value of any value raised to the zeroth power is 1. (Check this out in your high-school algebra book.)
The exponent and the factor
Hopefully, at this point you will understand the relationship between the exponent and the factor introduced earlier in Figure 3 .
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