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Please switch off your mobile phones 1 Data Representation Instructor: Mainak Chaudhuri [email protected] 2 Agenda • Recap • Talking to the computer – Numbers • Data types – Integer and long integer – Floating-point and double – Character and String – Boolean 3 Recap • • • • • Algorithms Programs Compilers: executables (binary: 0 and 1) Operating systems Central processing unit (CPU) and memory 4 Numbers • How does computer understand numbers? – Knows only two symbols – We are mostly familiar with decimal numbers – General number representation in arbitrary base – An algorithm for converting between bases – Special case: base=2 (binary) – Is there a decimal to binary converter inside the computer? Compiler does it – Negative numbers? • Two representation conventions: sign-magnitude representation and 2’s complement representation 5 2’s complement • Steps involved in converting decimal to 2’s complement – Decide the number of bits (should be at least 2+integer part of log2|N|) – Write the magnitude in binary and append zeros at the front to fill up the remaining bits (this is 2’s complement of the positive number) – Flip all bits (this is 1’s complement of the positive number) – Add 1 to it (this is 2’s complement representation of the negative number) 6 2’s complement • 2’s complement to decimal: – Write down the polynomial expansion in base 2 – Append a negative sign to the leading coefficient • Comparison of 2’s complement and signmagnitude – Range in sign-magnitude with n bits – Range in 2’s complement with n bits – Benefits of 2’s complement in binary arithmetic: will discuss later – All computers and calculators use 2’s complement representation 7 Variables • Anything that stores a value – Symbols made up of characters: A-Z, a-z, 09, _, $, … – Called identifiers – Must start with a letter or _ or $ – Examples: dayOfTheWeek, day_of_the_week, dayoftheweek, _dayoftheweek, myname, myName, … – Constants are not variables: 7, 100, 2.5, … – Variables are useful for holding non-constant values 8 Data types • Integer and Long integer – int and long – Called keywords: will learn more keywords – Keywords cannot be used as identifiers – Example: int x; – x is the variable name which we have declared as an integer – x is said to be of type integer – “int” must be written in small characters – This is called syntax of a language 9 – Not following it properly leads to syntax errors Data types • Floating-point and double – Used for representing non-integer numbers – Examples: float pi, _run_rate, Average_score; double e, interestRate; – pi, _run_rate, Average_score, e, interestRate are variable names – Notice the comma separating the names 10 Why data types? • Why can’t I just use a variable in computation? – Every variable must have a type – Why must it be declared to have a type? – Allocation in the memory (recall the scratchpad) – Every variable should get some space in the rough sheet; otherwise how can you use it for computation? – Help the compiler decide how many bits should be reserved for a variable – Observation: compiler must know the data 11 type to size mapping More data types • Character and String – Non-numeric variables – You may be surprised: we will see nonnumeric variables in computing – Examples: char orange; String something; – orange and something are variable names – Note the syntax – char is used to store a single symbol e.g. ‘f’, ‘2’, ‘$’, ‘ ‘, … – String is used to store a sequence of 12 symbols e.g. “My name is Mainak.” Even more data types • Boolean – – – – Can take two values only: true or false true and false are two boolean constants You may be surprised to see this type Can’t I declare boolean variables as integers? 13 • Integer Constants 1, 234, -56, 0, … • Floating-point and double 4.5, 56.789, 3.14, 2.71, 0.693, 4.5e3, 45000e-1 • Character ‘a’, ‘_’, ‘ ‘, ‘A’, ‘m’, ‘$’, … • String “Hi there”, “How are you?”, “This is esc101!!” • Boolean true, false • You can assign a constant value to a 14 variable: how? Will learn in next class