Integer Types

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Integer Types
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Bits and bytes

• A bit is a single two-valued quantity yes or no,
  true or false, on or off, high or low, good or
  bad
• One bit can distinguish between two cases T, F
• Two bits can distinguish between four cases TT,
  TF, FT, FF
• Three bits can distinguish between eight cases
  TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF
• In general, n bits can distinguish between 2n
  cases
• A byte is 8 bits, therefore 28 256 cases

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Number systems

• The binary (base 2) number system uses two
  binary digits, (abbreviation bits) -- 0 and 1
• The octal (base 8) number system uses eight
  digits 0, 1, 2, 3, 4, 5, 6, 7
• The decimal (base 10) number system uses ten
  digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• The hexadecimal, or hex (base 16) number system
  uses sixteen digits 0, 1, 2, 3, 4, 5, 6, 7, 8,
  9, A, B, C, D, E, F

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Everything is a number?

• Everything in the computer is stored as a pattern
  of bits
• Binary distinctions are easy for hardware to work
  with
• Numbers are stored as a pattern of bits
• Computers use the binary number system
• Characters are stored as a pattern of bits
• One byte (8 bits) can represent one of 256
  characters
• So, is everything in the computer stored as a
  number?
• No it isnt, its stored as a bit pattern
• There are many ways to interpret a bit pattern

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Counting

• To count up in any number system,
• add 1 to the rightmost digit
• if the result is higher than the largest digit,
• set that digit to zero and carry to the next
  place
• repeat addition of 1 and carrying as many times
  as necessary
• Example In hex, 4A6FF 1 4A700

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Computers use binary numbers

• People like to use decimal numbers
• Computers use binary numbers
• Java translates decimal numbers into binary
• The computer does all its arithmetic in binary
• Java translates binary results back into decimal
• You occasionally have to use numbers in other
  number systems

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Using octal and hex numbers

• Computers use binary, but the numbers are too
  long and confusing for people--its easy to lose
  your place
• Octal or hex is better for people
• Translation between binary and octal or hex is
  easy
• One octal digit equals three binary digits
• 101101011100101000001011
• 5 5 3 4 5 0 1 3
• One hexadecimal digit equals four binary digits
• 101101011100101000001011
• B 5 C A 0 B

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Writing octal and hex integers

• Integers are usually written in decimal notation
  7, 532, -28
• To write a number in octal, just start with a
  zero 02, 0657, -077
• but dont use the digits 8 or 9 !
• To write a number in hexadecimal, start with 0x
  or 0X 0xA, 0X43AB5, -0xFFFF
• the digits A through F can be upper or lower
  case

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Integer types

• There are four integer types
• byte occupies one byte (surprise!)
• can hold numbers in range 128 to 127
• short occupies two bytes
• can hold numbers in range 32768 to 32767
• int occupies four bytes
• can hold numbers up to or 2 billion
• long occupies eight bytes
• can hold numbers up to about 19 digits
• literals are written with a L suffix 123456789L

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Floating-point literals

• Floating-point literals are written with a
  decimal point 8.5 -7.923 5.000
• Floating-point numbers may also be written in
  scientific notation times a power of 10
• We use E to represent times 10 to the
• Example 4.32E5 means 4.32 x 105
• float literals are written with a F suffix
• Examples 8.5F -7.923F 5.000F
  4.32E5F
• If you dont have the F suffix, type double is
  assumed

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Floating point types

• There are two floating-point types
• float occupies four bytes
• Can hold numbers in the range 3.4E38 to 1.4E-45
• Accuracy is about nine digits
• double occupies eight bytes
• Can hold numbers in the range 1.7E308 to 4.9E-324
• Accuracy is seventeen or eighteen digits

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Number width

• Numeric types are considered wider or narrower
  than other numeric types
• This is based partly on number of bytes occupied
• Also based on how large a number it can hold
• Java doesnt mind if you assign a narrow value to
  a wide variable int n 3
• Java is not happy if you assign a wide value to a
  narrow variable byte b 7139946

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Widening and narrowing

• You can always assign a narrower value to a wider
  variable
• This is called widening
• You can do something special to assign a wide
  variable to a narrower variable
• This is called narrowing

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Casts

• You can convert (cast) one numeric type to
  another
• When you widen, no explicit cast is necessary
• But it doesnt hurt
• When you narrow, an explicit cast is required
• This requirement is made to help avoid errors
• Casting tells Java that the value in the wider
  type will fit in the narrower type
• Java checks to make sure that the cast works, and
  gives you an error if it didnt

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Example casts

• short s 0int i 0double d 0.0
• d i // legald s // legali s
  //legal
• i d // illegals d // illegals i
  // illegal

• i (int) d // legals (short) d //
  legals (short) i // legal
• d 3.7E20i 50000
• // The following give// runtime errorss
  (short) ii (int) d

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The End