Scala Binary Machine Arithmetic 1 21 2011 Opening Discussion Minute Essay comments Copy paste with middle click on Linux On Windows vi color coding Never touch the mouse Low learning curve in Scala Case sensitivity Going to the web for help Google Key Terms Token A set of characters that has meaning to the language Words Statement A set of tokens that give a complete instruction Sentences Expression Tokens put together that produce a value Phrases Type All values have types A type is a set of values and the operations allowed on them Literal A token that represents a value Numeric String Character Boolean Statements and Semicolon Inference In Scala as with most programming languages programs are made by putting together statements In Scala any expression is a valid statement as are a few other constructs Statements end with semicolons but they will be inferred at the end of a line if they make sense so you rarely type them Operators We can build longer expressions by putting literals together with operators Let s start off by playing with some of the numeric operations you are probably familiar with You can get the remainder after division with Objects An object is defined to be information along with the things you can do with that information The information in an object is called the properties The actions are called methods In Scala even things like Int are objects and have methods on them Methods The normal way to call a method in Scala and most other object oriented languages is to put a period after the object and follow it with the method name The REPL will do tab completion and list methods for you Let s look at the methods on some basic types and try calling them Arguments Some methods need additional information to work To give this to the method we pass in arguments Arguments are put in parentheses and separated by commas if there is more than one The parentheses are generally optional in Scala if there is no argument Operator Syntax All the operators in Scala are really just methods Scala allows any method with zero or one arguments to be called with an operator syntax That means you leave off the dot and the parentheses If a method takes no arguments you can call it without the dot Bases and Binary The decimal numbers we use are base 10 Each digit to the left is a higher power of 10 There is nothing special with decimal other than perhaps we have 10 fingers Other bases are equally valid Computers use binary numbers to store everything All digits are 0 or 1 and each position is a higher power of 2 toBinaryString Binary Addition Adding binary numbers is very easy Just do the long addition that you are used to You will carry a lot more frequently because anything above 1 causes a carry Let s run through some examples Consider implications of fixed precision Negative Numbers We don t have a in the computer for negative numbers All we have are 1 and 0 So how do we make negative numbers Remember the definition of negative numbers as additive inverse a a 0 We want to preserve this to keep addition simple This gives us 2s compliment numbers Binary Multiplication Multiplying binary numbers works just like long multiplication with decimals but easier My only recommendation is you only add two numbers at a time and take it in steps Hexadecimal Binary is unwieldy for humans because of the large number of digits Hexadecimal base 16 is commonly used because it converts nicely to binary but has few digits Four bits is a hex digit Start at the right and group bits by 4 Use letters A F for numbers 10 15 Hex literals start with 0x toHexString Octal Octal base 8 is less common than hex but not uncommon Group bits into groups of three Octal literals and toOctalString The math Object For other math functions use methods on the math object For example use math sqrt to take the square root of a number Minute Essay Convert 276 to binary We have our first quiz next class
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