Lecture 2: Topics

1. Lecture 2: Topics • Bits and Bytes • Primitive Types • Casting • Strings • Boolean expressions

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4. 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

5. 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

6. 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

7. 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)

8. 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

9. 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()

10. 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?

11. 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

12. 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 ?

13. 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?

14. 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

15. 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