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 2 E where E ranges from -126 to +127 and there are 23 bits available in the “significand” for bbb…bbb - (1.bbb….bbb) 2 x 2 E 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 2 E where E ranges from to and there are 52 bits available in the “significand” for bbb…bbb - (1.bbb….bbb) 2 x 2 E where E ranges from to 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 = require casting? Is the value of f the same as the value on the right-hand side? What about double f = ?

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