Lecture 2: Topics

• Bits and Bytes• Primitive Types• Casting• Strings• Boolean expressions

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Bits and Bytes

• A bit is either 0 or 1, “on” or “off”• A byte is ___ bits• A kilobyte is ___ bytes• A megabyte is ___ kilobytes• A gigabyte is ___ megabytes• A ______ is _____ gigabytes

Primitive Types• boolean: only 2 values: true and false• In principle, needs only a bit, but uses a byte

because of the way addressing is organized• char: 256 different possible character values.

Each char variable uses 1 byte• int: for signed whole numbers• Each int variable uses a 32-bit word• byte, short, long: 8, 16, 64-bit variants• float and double: for real numbers (not

necessarily whole numbers)• Each float (“floating point”) variable uses a 32-

bit word divided into 3 fields: sign, significand and exponent

• double (“double floating point”): 64-bit variant

int: possible values• Positive integers from 1 to ________,

represented by (0bbb…bbb)2 (31 bits are available for bbb…bbb)

• Negative integers from -1 to _______• _________• When System.out.println is used to print

the value of an int, it automatically calls a routine to convert the value from binary to decimal

• See Homework 1

float: possible values• + (1.bbb….bbb)2 x 2E where E ranges from -126

to +127 and there are 23 bits available in the “significand” for bbb…bbb

• - (1.bbb….bbb)2 x 2E where E ranges from -126 to +127 and there are 23 bits available in the “significand” for bbb…bbb

• Thus floats can store very large and very small numbers, but are limited to 23 “significant bits”: corresponds to about 7 decimal digits

• 0 (and -0 !)• Infinity and -Infinity• NaN (Not a Number)• The standard that defines this is called the IEEE

Floating Point Standard (1985)

double: possible values• + (1.bbb….bbb)2 x 2E where E ranges from -

1022 to +1023 and there are 52 bits available in the “significand” for bbb…bbb

• - (1.bbb….bbb)2 x 2E where E ranges from -1022 to +1023 and there are 52 bits available in the “significand” for bbb…bbb

• Thus doubles have an even bigger range AND have 52 significant bits: more than int. Corresponds to about 16 decimal digits

• ______• ______• ______• When System.out.println is used to print the

value of a float or double, it calls a conversion routine to convert the value from binary to decimal

More on float and double

• System.out.println(1 – 0.9) does not give exactly 0.1, because the computations are not exact: the answer is “rounded” to the closest “double” value to the exact answer, which is not exactly 0.9

• Notice that “doubles” are displayed to about 16 decimal digits by default, while “floats” are displayed to about 7 digits

• The Math class has constants such as Math.PI and (static) methods such as Math.sin(), Math.cos(), Math.exp()

The parallel resistance formula

• The resistance of a circuit with two resistors connected in parallel is

1/(1/R1 + 1/R2)• What happens if R1 = 0?

Mixing types in expressions• What is value of “1 / 2” ? ____• What is value of “1.0/2” ? ____• Type of the result is the “widest” type in

the expression• If the type of the identifier on the left-

hand side of an assignment statement has a narrower type than the expression on the right, it must be explicitly “cast” to the narrower type

Casting• Explicit “casting” is needed to convert a

wider type to a narrower type• Type width order: byte, short, int, long,

float, double (widest)• Example: float f = (float) Math.PI• Example: int i = (int) Math.PI• Does float f = 123456789 require

casting?• Is the value of f the same as the value on

the right-hand side?• What about double f = 123456789 ?

Converting char to int

• What happens:char x = ‘5’;int i = x;System.out.println(i);

• If want the integral value corresponding to character x:int i = x – ‘0’;

• Why is casting not needed?

Strings• A string is not a primitive data type• It is an object• Details later• For now, need to know about some

methods of the String class– String s; // s is a reference to a String object– s.length() is a call to a method that returns

the length of the string that s references– s.charAt(int j) is a call to a method that

returns the character at position j of the string that s references (first character is position 0, the last character is position s.length() – 1

Boolean expressions

• Comparison (relational) operators: >, >=, <, <=, ==, !=

• Boolean (logical) operators: !, ^, &&, ||, &, |

• Is this OK?public static boolean isLeapYear(int year){

return year % 4 == 0 && year % 100 != 0 || year % 400 == 0;

}

• Note: &&, || are “short-circuit” operators