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There are times when you use value types and times when you use reference types； just as
there are times when you pay for things using cash and times when you use a credit card。 Typi
cally though； you use credit cards when you want to pay for expensive things； because you
don’t want to carry around large amounts of cash。 This applies to value and reference types； in
that you don’t want to keep large footprint value types on the stack。
By knowing the difference between the stack and heap； you automatically know the differ
ence between a value type and a reference type； as they are directly related。 Value types are
stored on the stack； and the contents of reference types are stored on the heap。
Understanding the CLR Numeric Types
The CLR has two major types of numbers： whole numbers and fractional numbers。 Both of
these number types are value…based data types； as explained in the previous section。 The Add（）
method used the type Integer； which is a whole number–based value type。 As you saw； whole
numbers have upper limits； which are set by the space available。
Consider the following number：
123456
This number takes six spaces of room。 For illustrative purposes； imagine that the page you
are reading allows only six spaces of room for numerals。 Based on that information； the largest
number that can be written on this page is 999；999； and the smallest is 0。 In a similar manner；
specific number types force the CLR to impose restrictions on how many spaces can be used to
represent a number。 Each space is a 1 or a 0； allowing the CLR to represent numbers in binary
notation。
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44 CH AP T E R 2 ■ L E A R N IN G AB OU T 。 N E T N U M B E R A N D V A L U E T Y P E S
puters may use binary notations； but humans work better with decimals； so to calcu
late the largest possible number a data type can store； you use 2 to the power of the number of
spaces and then subtract 1。 In the case of the Integer type； there are 32 spaces。 Before we calculate
the biggest number Integer can store； though； we need to consider negative numbers。 The
upper limit of Integer isn’t actually 4；294；967；295 （the result of 232 – 1）； because Integer also
stores negative numbers。 In other words； it can save a negative whole number； such as –2。
The puter uses a trick in that the first space of the number is reserved for the sign （plus
or minus） of the number。 In the case of Integer； that means there are only 31 spaces for
numbers； so the largest number that can be represented is 2；147；483；647； and the smallest is
–2；147；483；648。 Going back to our addition example； this fact means that when the result of our
addition is 4 billion； which in binary requires 32 spaces； Integer does not have the space to store it。
The environment includes the numeric data types listed in Table 2…1； which have
varying sizes and storage capabilities。 The following terminology is used to describe numeric
data types：
o A bit is a space of storage； and 8 bits make a byte。
o Integers are whole numbers。
o Floating…point types are fractional numbers。
o Signed means one space in the number is reserved for the plus or negative sign。
Table 2…1。 Numeric Data Types
Type Description
Byte Unsigned 8…bit integer； the smallest value is 0； and the largest value is 255
SByte Signed 8…bit integer； the smallest value is –128； and the largest value is 127
UShort Unsigned 16…bit integer； the smallest value is 0； and the largest value is 65535
Short Signed 16…bit integer； the smallest value is –32768； and the largest value is 32767
UInteger Unsigned 32…bit integer； the smallest value is 0； and the largest value is
4294967295
Integer Signed 32…bit integer； the smallest value is –2147483648； and the largest value is
2147483647
ULong Unsigned 64…bit integer； the smallest value is 0； and the largest value is
18446744073709551615
Long Signed 64…bit integer； the smallest value is –9223372036854775808； and the
largest value is 9223372036854775807
Single 32…bit floating…point number； the smallest value is –3。4x1038； and the largest
value is 3。4x1038； with a precision of 7 digits
Double 64…bit floating…point number； the smallest value is –1。7x10308； and the largest
value is 1。7x10308； with 15 to 16 digits of precision
Decimal Special 128…bit data type； the smallest value is 1。0x10–28； and the largest value is
1。0x1028； with at least 28 significant digits of precisiona
a The Decimal type is often used for financial data because sometimes a calculation will result in one penny
less than the correct result （for example； 14。9999； instead of 15。00） due to rounding errors。
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CH A PT E R 2 ■ L E A R N I N G A B OU T 。 N E T N U M B E R AN D V A L U E T Y P E S 45
With so many variations of number types available； you may be wondering which ones to
use and when。 The quick answer is that it depends on your needs。 When performing scientific
calculations； you probably need to use a Double or Single。 If you are calculating mortgages； you
probably need to use a Decimal。 And if you are performing set calculations； you probably should
use an Integer or a Long。 It all depends on how accurate you want to be； or how much numeric
precision you want。
Numeric precision is an important topic and should never be dealt with lightly。 Consider
the following example： every country takes a census of its people； and when the census is
piled； we learn some interesting facts。 For example； in Canada； 31％ of people will divorce。
Canada has a population clock that says every minute and 32 seconds； someone is born。 At the
time of this writing； the population was 32；789；736。 Thus； at the time of this writing； 10；164；818
people will divorce。 Think a bit about what I just wrote。 I said that there is a direct relationship
of people who will divorce to the number of births in Canada （31％； in fact）。 You should be
amazed that the births and divorces are timed to the point where 10；164；818—not 10；164；819
nor 10；164；820—people will divorce。 Of course； I’m being cynical and just trying to make the
point that numbers are just that： numbers that you round off。
I can’t say 10；164；818 people will divorce； because I can’t be that accurate without performing
an actual count。 I could probably say 10；164；818 plus or minus 100；000 will divorce。 Using the
plus or minus； the range is 10；064；818 to 10；264；818； or roughly speaking； 10。2 million people。
The number 10。2 million is what a newsperson would report； what literature would say； and
what most people would use in conversation。 So； if I add 10。2 million and 1；000； can I say that
the total is 10；201；000？ The 10。2 is a roundoff to the nearest tenth of a million； and adding a
thousand means adding a number that is less than the roundoff。 The answer is that I cannot
add 1；000 to 10。2； because the 1；000 is not significant w