Week 1: Data Types & Representation

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# Week 1: Data Types & Representation > **BSCS1001 — IIT Madras BS Degree** **Prerequisite:** Topic 01 (What is Computational Thinking) **Cross-links:** BSCS1002-Python (Week 1 — Data Types), BSCS2002-PDSA (Week 2 — Data Structures) ## 1. Motivation: Why Data Types?

Week 1: Data Types & Representation

BSCS1001 — IIT Madras BS Degree Prerequisite: Topic 01 (What is Computational Thinking) Cross-links: BSCS1002-Python (Week 1 — Data Types), BSCS2002-PDSA (Week 2 — Data Structures)

1. Motivation: Why Data Types?

Imagine you receive a form with the following fields filled in:

Field	Value	Is This OK?
Name	`Rahul123!@#`	❌ Names shouldn't have numbers or special chars
Age	`-5`	❌ Age can't be negative
Marks	`108`	❌ Marks can't exceed 100
Phone	`hello`	❌ Phone should be digits

You can spot these errors because you know what kind of data each field should contain. But a computer doesn't — unless we tell it. Data types are the mechanism we use to tell the computer (or another person) what values are allowed and what operations are permitted.

Real-world analogy: A "data type" is like a mold for a key. The mold determines what shape keys can be made (allowed values) and what locks they can open (allowed operations).

What a Data Type Defines

(Diagram)

2. Sanity of Data

Sanity of data means checking that data makes sense — that values are within expected ranges and operations are meaningful.

Two Kinds of Constraints

1. Value Constraints (What values are allowed?)

Data Field	Allowed Values	Why?
Marks	0 to 100	Can't score more than 100 or less than 0
Gender	M or F	Only two values (in our dataset)
Name	Letters, spaces	No numbers or special characters
Date	0 to 365	Day of year

2. Operation Constraints (What can we do?)

Data	Allowed Operations	Not Allowed
Marks	`+` (add), `<` (compare)	`×` (multiplying marks is meaningless)
Name	`=` (compare for equality)	`+` (can't add two names)
Gender	`=` (check if equal)	`+`, `-` (meaningless)

Worked Example: Sanity Check

Problem: Check if a student record is valid. Record: {Name: "Alice", Age: 22, Maths: 85, Physics: 110}

Field	Sanity Rule	Check	Verdict
Name	Only letters and spaces	"Alice" ✅	Valid
Age	Between 0 and 150	22 ✅	Valid
Maths	Between 0 and 100	85 ✅	Valid
Physics	Between 0 and 100	110 ❌	Invalid

💡 Key Insight: Sanity of data leads directly to the concept of data types. Once we define types, sanity checks become automatic.

3. Basic Data Types

The course defines three basic data types (plus a fourth — String — which is a sequence of characters).

3.1 Boolean

The simplest data type. Named after George Boole, a mathematician.

Property	Description
Values	`True` or `False` only
Operations	AND, OR, NOT
Result type	Boolean

Boolean Operations (Truth Tables)

AND (AND): True only when BOTH inputs are True.

A	B	A AND B
False	False	False
False	True	False
True	False	False
True	True	True

OR (OR): True when AT LEAST ONE input is True.

A	B	A OR B
False	False	False
False	True	True
True	False	True
True	True	True

NOT (NOT): Flips the value.

A	NOT A
True	False
False	True

Worked Example: Boolean Evaluation

Evaluate: (True AND False) OR (NOT False)

Step	Expression	Result
1	`True AND False`	`False`
2	`NOT False`	`True`
3	`False OR True`	`True`

3.2 Integer

Whole numbers (positive, negative, and zero).

Property	Description
Values	`..., -3, -2, -1, 0, 1, 2, 3, ...`
Operations	`+`, `-`, `×`, `/` (result: Integer)
Comparisons	``, `=` (result: Boolean)

Integer Operations Examples

Operation	Result	Data Type of Result
`3 + 5`	`8`	Integer
`10 - 7`	`3`	Integer
`4 × 6`	`24`	Integer
`7 < 3`	`False`	Boolean
`5 = 5`	`True`	Boolean

⚠️ Note: In this course, integer division / may produce non-integer results, so we mostly use +, -, × for integers.

3.3 Character

A single letter, digit, or symbol.

Property	Description
Values	A–Z, a–z, 0–9, special characters
Operations	`=` (compare for equality)
Result type	Boolean

Examples of characters: 'A', 'z', '5', '?', ' ' (space) Special characters: , ; : * / & % $ # @ !

3.4 String

A sequence of characters.

Property	Description
Values	Any sequence of characters, e.g., `"Hello"`, `"Alice"`, `"M"`
Operations	`=` (equality), `char in string?` (checking membership)
Result type	Boolean; Boolean

Key difference: A Character is a single symbol, a String is a sequence of zero or more characters.

4. Subtypes

A subtype is a more restricted version of a basic type. It limits the allowed values and/or operations.

Why Subtypes?

A plain Integer is too broad. Consider:

Marks: Should be 0–100, not any integer
Count: Should be 0 or positive, not negative
Date: Should be 0–365, not any integer Subtypes allow us to create more specific, meaningful types.

Integer Subtypes

SeqNo (Sequence Number)


pseudo
Range:     0, 1, 2, ..., Max (e.g., 10000)
Operations: None of the integer operations make sense
Purpose:   Identifies a card/row uniquely

Marks


pseudo
Range:     0, 1, 2, 3, ..., 100
Operations: +, - (result: Marks);  <, >, = (result: Boolean)
NOT allowed: ×, ÷ (multiplying marks makes no sense!)

Count


pseudo
Range:     0, 1, 2, 3, ...
Operations: +, - (result: Count); <, >, = (result: Boolean)
NOT allowed: ×, ÷

Date (Day of Year)


python
Range:     0, 1, 2, 3, ..., 365
Operations: print (result: String); <, >, = (result: Boolean)
Meaning:  0 = "1 Jan", 31 = "1 Feb", 365 = "31 Dec"

Character Subtypes

Gender


pseudo
Values:    'M' or 'F'
Operation: = (compare)
Result:    Boolean

String Subtypes

Names


pseudo
Values:    Strings with no special characters
Operation: =
Result:    Boolean

City


pseudo
Values:    Strings with no special characters
Operation: =
Result:    Boolean

Words


pseudo
Values:    Strings with alphanumeric and punctuation
Operation: =
Result:    Boolean

Subtype Hierarchy Diagram

(Diagram)

5. Type Transformations

Sometimes we need to convert data from one type to another.

Date to String Transformation

Dates are stored as integers (0–365) but displayed as strings.

Integer Value	Display String
0	"1 Jan"
31	"1 Feb"
59	"1 Mar"


python
print(0)   →  "1 Jan"
print(31)  →  "1 Feb"
print(365) →  "31 Dec"

Fractional Marks Transformation

In this course, we avoid floating-point numbers by scaling:

Actual mark: 62.5
Stored as integer: 6250 (multiply by 100)
Display: print(6250) → "62.5" (divide by 100 when printing)


pseudo
Value to store = Original mark × 100
Display value  = Stored value ÷ 100

Example:

Original	Scaled (×100)	Stored Type	Operation	Printed
76.25	7625	Integer	+, -	"76.25"
82.5	8250	Integer	+, -	"82.5"
91.0	9100	Integer	+, -	"91.0"

Why do this? Integers are simpler, faster, and avoid rounding errors that occur with decimal numbers.

6. Records: Grouping Data Together

A Record (also called struct or tuple) is a data type with multiple named fields, each of which has a name and a value.

Record Example: Marks Card

(Diagram)

Why Records?

Without records, we'd need separate variables for every attribute of every student, which is impossible for a class of 200.

Without Records	With Records
`Alice_Maths`, `Bob_Maths`, `Charlie_Maths`...	Each card `X` has `X.Maths`
Need 200 variables for each subject	One record type, many instances
Cannot write generic procedures	Can write procedures that work on any card

Accessing Record Fields

We use dot notation: RecordName.FieldName


pseudo
X.Maths     ← The Maths field of card X
X.Name      ← The Name field of card X
X.Gender    ← The Gender field of card X

Other Record Examples

Word in Paragraph Record

Field	Data Type
SerialNo	SeqNo
Word	Words
PartOfSpeech	Category

Shopping Bill Record

Field	Data Type
CustomerName	Names
ItemName	Words
Category	Category
Quantity	Count
Amount	Marks (type, for cost)

7. Lists: Sequences of Data

A List is a sequence of data elements, all of the same type.

List vs Record

Record	List
Groups different types of data	Groups same type of data
Fields have names	Elements have positions
Example: A single student's data	Example: All students' IDs

Examples of Lists

List Name	Element Type	Description
`MarksCardList`	MarksCard Record	All marks cards in the dataset
`ParagraphWordList`	WordInPara Record	All words in a paragraph
`ShoppingBillList`	ShoppingBill Record	All shopping bills
`ItemList`	Item Record	Items in a single bill

Visual Representation


pseudo
MarksCardList = [Card1, Card2, Card3, ..., CardN]
                  ↑       ↑       ↑           ↑
                 SeqNo=1 SeqNo=2 SeqNo=3    SeqNo=N

Key Point About Lists

All elements in a list are usually of the same data type
Lists can be iterated over (the iterator pattern from Topic 01)
Lists can be built gradually by appending elements

Preview: We'll work extensively with lists starting in Week 5. For now, just understand that a list is a collection of items arranged in a specific order.

8. Comparison of Data Types

Basic Data Types Summary Table

Type	Values	Operations	Result Types	Use Case
Boolean	True, False	AND, OR, NOT	Boolean	Conditions, flags
Integer	..., -2, -1, 0, 1, 2, ...	+, -, ×, /, , =	Integer, Boolean	Counts, sums, indices
Character	A-Z, a-z, 0-9, special chars	=	Boolean	Single letters, gender codes
String	Any character sequence	=, char-in-string?	Boolean	Names, words, categories

Type vs Subtype

Aspect	Basic Type	Subtype
Range	Broad (e.g., all integers)	Restricted (e.g., 0-100)
Operations	All type operations	Subset of operations
Example	Integer → Marks	Marks: 0-100, no ×, ÷

Record vs List

Aspect	Record	List
Structure	Named fields	Positional elements
Element types	Can be different	Same type preferred
Access	By field name: `X.Name`	By position
Analogy	A row in a table	The whole table

9. Practice Questions

Basic Questions

Q1. Which basic data type has only two possible values?

Show Answer

Boolean — values are True and False. Q2. Evaluate: (NOT (True AND False)) OR (False AND True) Show Answer

Step	Expression	Result
1	`True AND False`	`False`
2	`NOT False`	`True`
3	`False AND True`	`False`
4	`True OR False`	`True`

Q3. What is the range of values for the Marks subtype?

Show Answer

Marks range from 0 to 100 (inclusive). Q4. Which of these operations are allowed on a Gender field? (a) + (b) = (c) × (d) < Show Answer

Only (b) = (comparison for equality) is allowed on Gender. Arithmetic operations like +, ×, < are meaningless.

Intermediate Questions

Q5. What is wrong with storing marks as a plain Integer data type? Why do we need a Marks subtype?

Show Answer

If marks are stored as Integer, the computer would allow:

Negative marks (-5) → invalid

Marks above 100 (150) → invalid

Multiplication of marks → meaningless

A Marks subtype restricts:

Range to 0-100

Operations to +, -, <, >, = only (no ×, ÷) Q6. Convert these fractional marks to their scaled integer representation: (a) 45.75 (b) 80.0 (c) 99.99 Show Answer

Original	Scaled (×100)
45.75	4575
80.0	8000
99.99	9999

Q7. If Date values are stored as integers 0-365, what date does value 59 represent? (Hint: 0 = 1 Jan, 31 = 1 Feb)

Show Answer

0 = 1 Jan (31 days in January)

31 = 1 Feb (28 days in February in non-leap year)

31 + 28 = 59 = 1 March Q8. What is the difference between a Record and a List? Give one example of each. Show Answer

Aspect	Record	List
Fields	Named (e.g., `X.Name`, `X.Maths`)	Positional (by index)
Types	Can mix types	Usually same type
Example	A single MarksCard (has Name, Maths, Physics, etc.)	MarksCardList (all cards together)

Advanced Questions

Q9. Design a Record type for a Library Book. What fields would it have and what data types/subtypes would each field use?

Show Answer


java
Record: Book
    - BookID:        SeqNo (unique identifier)
    - Title:         String (book name)
    - Author:        Names (author name)
    - ISBN:          String (unique book number)
    - YearPublished: Integer (subtype: 1900-2024)
    - Pages:         Count (number of pages)
    - IsIssued:      Boolean (True if checked out)
    - Category:      String (subtype: Fiction/Non-fiction/Reference)

Q10. Can you add two Names together? Can you compare two Names with =? Explain why or why not for each.

Show Answer

= (equality): ✅ Yes! We can check if two names are the same (e.g., "Alice" == "Alice" → True). Result is Boolean.

+ (addition): ❌ No! Adding names doesn't make sense — what would "Alice" + "Bob" mean? Names are identifiers, not quantities.

This is exactly what data types enforce: only meaningful operations are allowed. Q11. Explain why marks × marks is not allowed but marks + marks is allowed. Show Answer

marks + marks: Adding marks makes sense — we sum scores to get a total. The result is also of type Marks (or Total).

marks × marks: Multiplying marks has no real-world meaning. What would "85 × 72" represent? It's not a score, not a count, nothing useful. The Marks subtype correctly forbids this.

This illustrates the key principle: data types model real-world constraints. Q12. Trace the Boolean expression: (A OR B) AND (NOT A) for all four combinations of A and B. Show Answer

A	B	A OR B	NOT A	(A OR B) AND (NOT A)
F	F	F	T	F
F	T	T	T	T
T	F	T	F	F
T	T	T	F	F

The expression is True only when A is False AND B is True.

📚 Cross-References

Course	Topic	Connection
BSCS1002 (Python)	Week 1 — Data Types	Python's `int`, `bool`, `str` types
BSCS1002 (Python)	Week 2 — Operators	Boolean operators in Python
BSCS2002 (PDSA)	Week 1 — Abstract Data Types	Formal definition of types

Next Topic: 03 — Pseudocode Basics

Quiz Tip: Questions about allowed operations on specific data types are very common in Quiz 1. Memorize the operation tables! Join Discord PreviousWhat is Computational Thinking?NextPseudocode Basics

What this note is really saying

Week 1: Data Types & Representation

1. Motivation: Why Data Types?

What a Data Type Defines

2. Sanity of Data

Two Kinds of Constraints

1. Value Constraints (What values are allowed?)

2. Operation Constraints (What can we do?)

Worked Example: Sanity Check

3. Basic Data Types

3.1 Boolean

Boolean Operations (Truth Tables)

Worked Example: Boolean Evaluation

3.2 Integer

Integer Operations Examples

3.3 Character

3.4 String

4. Subtypes

Why Subtypes?

Integer Subtypes

SeqNo (Sequence Number)

Marks

Count

Date (Day of Year)

Character Subtypes

Gender

String Subtypes

Names

City

Words

Category

Subtype Hierarchy Diagram

5. Type Transformations

Date to String Transformation

Fractional Marks Transformation

6. Records: Grouping Data Together

Record Example: Marks Card

Why Records?

Accessing Record Fields

Other Record Examples

Word in Paragraph Record

Shopping Bill Record

7. Lists: Sequences of Data

List vs Record

Examples of Lists

Visual Representation

Key Point About Lists

8. Comparison of Data Types

Basic Data Types Summary Table

Type vs Subtype

Record vs List

9. Practice Questions

Basic Questions

Intermediate Questions

Advanced Questions

📚 Cross-References

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