COS 140: Foundations of Computer Science - University of...

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COS 140: Foundations of Computer Science

Variables and Primitive Data Types

Fall 2017

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Foundations

Homework

Introduction

Variable names

Assignment

Data types

Primitive data types


• Reading: Chapter 16

• Homework: Exercises at end of chapter

• Homework due 10/23

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Foundations

What is a variable?

Introduction

• What is a variable?

• Variable attributes

• Binding

Variable names

Assignment

Data types



• In this lecture: imperative/OO languages

• A variable is an area of memory that:

◦ can have a value

◦ can have its value changed by the program

• Different sizes: byte, word, multiple words

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Foundations

Variable attributes

Introduction



• Binding

Variable names

Assignment

Data types



• Name – what do we call it?

• Address – where does it live in memory?

• Type – what kind of thing can it hold?

• Value – “contents” of the variable

• Scope – who can see this variable?

• Lifetime – duration of program, or shorter period?

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Foundations

Binding

Introduction



• Binding

Variable names

Assignment

Data types



• Associates an attriburte value with an attribute

• Not just “value” attribute

• Two types:

◦ Static binding: occurs before run-time, not changed afterward

• Allows compiler to check for errors, but...

• ...need information about the binding at compile time

◦ Dynamic binding: takes place/is changed at run-time

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Foundations

Variable names

Introduction

Variable names

• Variable names

• Name length

• Special names

Assignment

Data types



• Name: identifier associated variable

• Same name⇔ different variables in different contexts

• Different names⇔ same variable

• Unnamed variables: access via pointer

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Foundations

Variable names

Introduction

Variable names

• Variable names

• Name length

• Special names

Assignment

Data types



• Strings (symbols) in a symbol table

• Symbol tables created at compile/interpretation time

• Associate names with entities (e.g., variables)

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Foundations

Variable names

Introduction

Variable names

• Variable names

• Name length

• Special names

Assignment

Data types



• Which characters to allow?

• Have to recognize names during lexical analysis⇒ no spaces

• Sometimes special initial character – e.g., a letter

• For enhanced readability, may allow connectors (e.g., “-”, “ ”),

case-sensitivity

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Foundations

Length of variable names

Introduction

Variable names

• Variable names

• Name length

• Special names

Assignment

Data types



• Names should be meaningful⇒ longer names

• But symbol table should be reasonable size, easy to maintain⇒

shorter names

• BASIC: one letter + optional number

◦ Can’t complain about the size!

◦ Readable for mathematical applications, but not much else

• Limited number of characters – e.g., FORTRAN (6 or 31), C (63

significant)

◦ Trades-off readability and wasted space

◦ Table maintenance easy, but whatever the size, someone

always wants more

• Unlimited number of characters – e.g., Ada, Lisp

◦ Complete flexibility, but...

◦ ...potentially great deal of space, hard to maintain

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Foundations

Special names

Introduction

Variable names

• Variable names

• Name length

• Special names

Assignment

Data types



• Some names not allowed or limited

• Reserved words – can only be used in language-defined

context(s) – if in C, e.g.

• Predefined words – defined in the language, but can be changed

(e.g., Ada, C [libraries])

• Keywords – special meaning in some contexts, but can be used

as a name (e.g., for in Lisp, if in FORTRAN)

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Foundations

Giving variables values

Introduction

Variable names

Assignment

Data types



• Assignment construct binds a value to a variable

• Often, a construct such as: x = a+ b

◦ x’s value is bound to result of a+ b

◦ Not algebra: can have: x = x+ 1

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Foundations

Assignment construct examples

Introduction

Variable names

Assignment

Data types



C, Java, Python... x = x + 1;

Pascal x := x + 1

Lisp (setf x (1+ x))

R x <<- x + 1 or x + 1 -> x

Smalltalk x ← x + 1

Forth x 1 + x !

COBOL ADD X 1 GIVING X

TCL set x x + 1

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Foundations

Data types

Introduction

Variable names

Assignment

Data types



• All data has a type: integer, floating point, etc.

• Type species size, interpretation, operations for data

• All variables have a type attribute

• Depending on language, variables’ type static or dynamic

• Determining variable type:

◦ Declared somewhere in program (static, explicit)

◦ Inferred by compiler/interpreter (static, implicit; dynamic)

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Foundations

What are primitive data types?

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• Primitive data types: defined by language

• Not (usually) defined in terms of other types

• Building blocks of new types

• Unstructured/atomic data types (scalars):

◦ Integers

◦ Floating point numbers

◦ Booleans

◦ Characters

◦ Pointers

• Structured data types:

◦ Strings

◦ Arrays

◦ Records

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Foundations

Integers

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• Integer type represents subset of the integers Z (duh)

• Most common data type

• You’ve seen: sign-magnitude, two’s complement

• Most languages: several sizes (byte, 2 byte, 4 byte...)

◦ Can’t represent all possible integers in computer – instead

i . . . j, where i ≤ 0 ≤ j

◦ For two’s complement, with n bits, can represent

−2n−1 . . . 2n−1 − 1◦ E.g., 8 bits can represent 100000002 (= −12810) to

011111112 (= 12710).

• Some languages: unsigned integers (C)

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Floating point numbers

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• Represent subset of real numbers R

• Usually two sizes

• Two parts: fraction and exponent

◦ E.g.: 0.11012, exponent 1012

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Foundations


Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers





◦ E.g.: 0.11012, exponent 1012◦ Fractional part = 1

2 + 14 + 0

8 + 116 = 0.812510

CSomputer

cience

Foundations


Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers






2 + 14 + 0

8 + 116 = 0.812510

◦ Exponent = 5, so multiply fraction by 25

CSomputer

cience

Foundations


Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers






2 + 14 + 0

8 + 116 = 0.812510


◦ So number is 0.8125× 32 = 26.010

CSomputer

cience

Foundations


Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers






2 + 14 + 0

8 + 116 = 0.812510


◦ So number is 0.8125× 32 = 26.010

• Can’t represent all numbers accurately – e.g., π, 13

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Foundations

Booleans

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• True/false values

• Good for flags (switches), conditions to be checked

• Sometimes languages provide as primitive data type

• If not:

◦ 0 is false, everything else true (C)

◦ 0, ””, [], etc., is false, everything else is true (Python)

• Representation: smallest efficiently-addressable unit (often byte)

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Characters

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• Character represented as a pattern of 1s and 0s

• Representations:

◦ ASCII

• 7 bits code; 8-bit variants of this (e.g., ISO 8859–1) are the

most common codes used

• E.g.: “a” = 33, “b” = 34, ...; space = 32

◦ Unicode

• 16 bits (or longer); accommodates other alphabets and

symbols

• E.g.: - codepoints 47196, 51060; ;

◦ EBCDIC – 8 bits; old IBM code

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Foundations

Strings

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• Sequence of characters: textual data

• Special operators (e.g., substring, concatenation), special

relational operators, sometimes special assignment

• Lengths:

◦ Fixed length: always same size

◦ Limited-dynamic – can change, but there’s a maximum (e.g.,

C)

• Length + sequence (often array) of characters

• Null-terminated sequence of characters

◦ Dynamic – can change without limit (e.g., Lisp) – more

flexible, but overhead for allocation/deallocation

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Foundations

Arrays

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• Sometimes need to represent groups of related data items (e.g.,

integers, characters, etc.)

• An array is a data type that stores homogeneous data in

contiguous memory

• Can be single-dimensional (vectors) or multi-dimensional

• Use index to find element

• Value of index doesn’t affect time taken to find element⇒

random access storage

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Foundations

Design issues for Arrays

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• Syntax for array indices – e.g., Temperatures(20) or

Temperatures[20]

• Subscripts:

◦ what is the lower bound?

◦ bounds checking or not?

◦ must subscripts be integers?

• Number of dimensions allowed

◦ Usually no real limits

◦ C: limits to one dimension, but allows array elements to be

themselves arrays

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Foundations

Array descriptors

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• What information is needed by the programming

language/program about an array?

• Base address – where is the first element

• Element type

• Index type – doesn’t have to be integer for some languages

• Index lower, upper bounds

• Number of locations in array

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Foundations

Finding address of array element

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• Element location (or address, A) depends on base address (B),

index (I), index lower bound (L), and element size (S)

A = B + (I − L)× S

CSomputer

cience

Foundations


Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers




A = B + (I − L)× S

Given an array “Taxes” whose startlocation is 1024, element type is along integer (8 bytes), and whoseindices start at 0, find location ofelement Taxes[15] 1024

1028

1032

...

Array "Taxes"

Taxes[0]

Taxes[1]

Taxes[15]

CSomputer

cience

Foundations


Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers




A = B + (I − L)× S

Given an array “Taxes” whose startlocation is 1024, element type is along integer (8 bytes), and whoseindices start at 0, find location ofelement Taxes[15] 1024

1028

1032

...

Array "Taxes"

Taxes[0]

Taxes[1]

Taxes[15]

• A = 1024 + (15− 0)× 8 = 1144

CSomputer

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Foundations

Another example

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• Suppose array Foo has elements of a type that requires 6 bytes

to store, that it begins at location 4096, and that its indices begin

at 10.

• What is the address of Foo[201]?

CSomputer

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Foundations

Another example

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• Suppose array Foo has elements of a type that requires 6 bytes

to store, that it begins at location 4096, and that its indices begin

at 10.

• What is the address of Foo[201]?

• Answer:

A = B + (I − L)× S

= 4096 + (201− 10)× 6= 5242

CSomputer

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Foundations

Optimizing address computation

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• Can write expression so static parts can be calculated at compile

time and stored in a constant:

A = B + (I − L)× S= B + (I × S)− (L× S)= (I × S) + (B − L× S)← constant part

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Foundations

Multidimensional arrays

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• Can have more than 1 dimension• E.g., 10× 10 array is 2D, 100 entries, 10 rows, 10 columns• Indices: [row,column] or [row][column]• How to store dimensions?

◦ Row-major order: Rows are kept together, elements stored

one row after anotherT: array 1..10, 1..10 of integers

row 1

...row 2 row 10

◦ Column-major order: keeps columns together

• Row-major probably more common

CSomputer

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Foundations

Address calculation

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• Array T is an 2D array of temperatures taken over a 1-meter grid,

100 m on a side

• Assume row-major order, float data type (assume 4 bytes), base

address for T = 2048, indices each start at 0 (so 0..99)

• What is the address of T[20,15]?

CSomputer

cience

Foundations

Address calculation

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers



100 m on a side




• First: what is start of row 20?

A[20,0] = B + (I − L)× S

= 2048 + (20− 0)× (4× 100) = 10, 048

CSomputer

cience

Foundations

Address calculation

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers



100 m on a side




• First: what is start of row 20?

A[20,0] = B + (I − L)× S

= 2048 + (20− 0)× (4× 100) = 10, 048

• Next, find offset of element in row 20 – same kind of calculation:

A[20,15] = 10, 048 + (I − L)× S

= 10, 048 + (15− 0)× 4 = 10, 108

CSomputer

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Foundations

Heterogenous types: Records, structs

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• Records contain heterogeneous related data

• E.g., data about employee: name (string), address (string), salary

(fixed-point integer), height (float),...

• Most languages support this type: struct in C, defstruct in

Lisp, record in Pascal, etc.

• Design issues:

◦ How are fields selected?

◦ How is field checked?

◦ Can we assign one structure to another?

◦ How to implement – e.g., how to find element from selector?

(field must have type, offset)

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Foundations

Pointers

Introduction

Variable names

Assignment

Data types


• Numeric types

• Booleans

• Characters

• Arrays

• Records

• Pointers


• These “point” to an object: contain its address

• Used for user-created dynamic variables (from heap)

• Used for indirect addressing (e.g., C) – abstraction of assembly

language’s indirect addressing mode

• Can assign to and through them:

int a = 3; // integer

int* p; // pointer to integer

p = &a; // p = a’s address

*p = 4; // a now = 4

• Often used (in C, e.g.) to access array elements

int a[100]; // 100-element array of ints

int* p = a; // p = addr of a’s start (no &)

for (int i=0;i<100;i++) {

*p = 0;

p++;

}

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