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Data Representation
Instructor: Mainak Chaudhuri
[email protected]
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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
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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: 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
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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: makes logic design simpler
– All computers and calculators use 2’s
complement representation
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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
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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
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– 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
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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
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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’, ‘$’, ‘ ‘, …
– String is used to store a sequence of 12
symbols e.g. “My name is Tintin.”
Even more data types
• Boolean
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Can take two values only: true or false
true and false are two boolean constants
You may be surprised to see this type
Can’t I declare boolean variables as integers?
• Byte
– 8-bit integer
– Example: byte x;
– Range of x?
• Short
– 16-bit integer
– Example: short y;
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Constants
• Integer (int)
1, 234, -56, 0, …
• Floating-point and double (float, double)
4.5, 56.789, 3.14, 2.71, 0.693, 4.5e3, 45000e-1
• Character (char)
‘a’, ‘_’, ‘ ‘, ‘A’, ‘m’, ‘$’, …
• String (String)
“Hi there”, “How are you?”, “This is esc101!!”
• Boolean (boolean)
true, false
• You can assign a constant value to a 14
variable: how? Will learn in next class