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Data Representation

• Instructor Mainak Chaudhuri
• mainakc_at_cse.iitk.ac.in

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Agenda

• Recap
• Talking to the computer
• Numbers
• Data types
• Integer and long integer
• Floating-point and double
• Character and String
• Boolean

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Recap

• Algorithms
• Programs
• Compilers executables (binary 0 and 1)
• Operating systems
• Central processing unit (CPU) and memory

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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 base2 (binary)
• Is there a decimal to binary converter inside the
  computer? Compiler does it
• Negative numbers?
• Two representation conventions sign-magnitude
  representation and 2s complement representation

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2s complement

• Steps involved in converting decimal to 2s
  complement
• Decide the number of bits (should be at least
  2integer part of log2N)
• Write the magnitude in binary and append zeros at
  the front to fill up the remaining bits (this is
  2s complement of the positive number)
• Flip all bits (this is 1s complement of the
  positive number)
• Add 1 to it (this is 2s complement
  representation of the negative number)

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2s complement

• 2s complement to decimal
• Write down the polynomial expansion in base 2
• Append a negative sign to the leading coefficient
• Comparison of 2s complement and sign-magnitude
• Range in sign-magnitude with n bits
• Range in 2s complement with n bits
• Benefits of 2s complement in binary arithmetic
  will discuss later
• All computers and calculators use 2s complement
  representation

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Variables

• Anything that stores a value
• Symbols made up of characters A-Z, a-z, 0-9, _,
  ,
• 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

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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
• Not following it properly leads to syntax errors

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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

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Why data types?

• Why cant 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 type to
  size mapping

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More data types

• Character and String
• Non-numeric variables
• You may be surprised we will see non-numeric
  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 symbols
  e.g. My name is Mainak.

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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
• Cant I declare boolean variables as integers?

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Constants

• Integer
• 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 variable
  how? Will learn in next class