Notes, summaries, assignments, exams, and problems for Computers

1. Functional Dependency (FD)

A functional dependency A → B means: if you know the value of attribute A, you can always determine the value of attribute B. In other words, no two rows can have the same A value but different B values.

Example: In a table Student(StudentID, Name, Email): StudentID → Name, Email (Given a StudentID, the Name and Email are always uniquely determined.)

2. Boyce-Codd Normal Form (BCNF)

A relation is in BCNF if, for every functional dependency X → Y, X is a superkey.

• Compliance: Every determinant in the table is a candidate key—no changes needed.
• Evaluation: Whenever there is a non-trivial FD X → Y where X is not a superkey. This means some attribute depends on only part of a key, or on a non-key attribute—causing

Lecture 1: Moore's Law

Moore's Law: The number of transistors on microchips doubles every two years.

Lecture 2: Logic Gates

AND, OR, and NOT gates are universal.

Logic word problem steps:

Example: In a bank, there were four employees: the bank manager, assistant manager, teller, and the security guard. The bank has a single vault for the storage of their money. This vault was designed so that it needs four signals to open it. These four signals are from the bank manager, assistant manager, teller, and the security guard. For the vault to open, it needs the following conditions:

1. No single employee can open the vault.
2. It can be opened with three employees as long as one of them is the manager.
3. It can be opened by the manager together with the assistant

Q1. Array Address Calculation (Row & Column Major)

Problem: An array ARR[-5...15, 10...20] stores elements in Row Major with each element requiring 2 bytes. Base address is 2500. Find the address of ARR[10][15].

Answer:

• Row range: -5 to 15, so Lr = -5, Ur = 15
• Column range: 10 to 20, so Lc = 10, Uc = 20
• Element size (w) = 2 bytes
• Base Address (BA) = 2500

Step 1: Calculate dimensions

• Number of rows (M) = Ur - Lr + 1 = 15 - (-5) + 1 = 21
• Number of columns (N) = Uc - Lc + 1 = 20 - 10 + 1 = 11

Step 2: Row Major Order Formula

Address(A[i][j]) = BA + [(i - Lr) × N + (j - Lc)] × w
Address(ARR[10][15]) = 2500 + [(10 - (-5)) × 11 + (15 - 10)] × 2
= 2500 + [15 × 11 + 5] × 2
= 2500 + [165 + 5] × 2
= 2500 + 170 × 2 = 2840

Step 3: Column Major Order Formula

Address(... Continue reading "Data Structures and Algorithms Practice Problems" »

Here is a complete and concise answer sheet for your Digital Electronics CIE-1 preparation based on your questions:

1. Design Half and Full Subtractor with Truth Table

Half Subtractor

• Inputs: A, B
• Outputs: Difference (D), Borrow (Bo)
• Logic Equations:
  • Difference (D) = A ⊕ B
  • Borrow (Bo) = A' · B

Full Subtractor

• Inputs: A, B, B_in (Borrow In)
• Outputs: Difference (D), Borrow Out (B_o)
• Logic Equations:
  • D = A ⊕ B ⊕ B_in
  • B_o = B · B_in + B · A' + A' · B_in

2. Working of Adder and Subtractor

Adder Circuits

• Half Adder: Adds two bits A and B.
  • Sum = A ⊕ B, Carry = A · B
• Full Adder: Adds three bits A, B, and C_in.
  • Sum = A ⊕ B ⊕ C_in, C_out = AB + AC_in + BC_in

Subtractor Circuits

• Half Subtractor: Subtracts B from A.
  • Difference = A ⊕ B, Borrow = A' · B
• Full Subtractor:

Recursive Functions in Python

def range_sum(num_list, start, end):
    if start > end:          # Base case
        return 0
    else:                    # Recursive case
        return num_list[start] + range_sum(num_list, start + 1, end)

numbers = [2, 4, 6, 8, 10]
print(range_sum(numbers, 1, 3))  # Expected output: 18

Tower of Hanoi

def hanoi(n, from_peg, to_peg, temp_peg):
    if n > 0:
        # Step 1: Move n-1 discs to temp peg
        hanoi(n - 1, from_peg, temp_peg, to_peg)
        # Step 2: Move the bottom disc
        print(f"Move disc from peg {from_peg} to peg {to_peg}")
        # Step 3: Move n-1 discs from temp peg to target peg
        hanoi(n - 1, temp_peg, to_peg, from_peg)

Greatest Common Divisor

def gcd(x, y):
    if x

Logical Volume Management (LVM) in Linux Storage

F. The the vast realm of operating systems, Linux has emerged as a robust and versatile choice, powering everything from personal computers to enterprise-level servers. One of its standout features is Logical Volume Management (LVM), a powerful storage management system that offers enhanced flexibility, scalability, and reliability for handling storage devices in Linux environments. LVM revolutionizes how disk partitions and physical storage are managed, providing an abstract layer that simplifies storage administration and facilitates efficient utilization of available resources. By introducing logical volumes, volume groups, and physical volumes (PVs) (originally referred to as "physical books"... Continue reading "Mastering LVM: Dynamic Storage Management in Linux" »

Domain Model

• Shows concepts only: classes, attributes, associations, and multiplicities.
• No methods, no UI, and no controllers are included.
• Purpose: To understand the real-world objects involved in the system.

Use Case Model (Module 6)

• Focuses on Actor ↔ System interaction.
• Uses the Verb + Noun naming convention.
• Format: Defines Actor steps versus System steps.
• Use cases serve as input for sequence diagrams, which inform class diagrams.

UML Class Diagram (Module 7)

• Class Components: Name, attributes, and methods.
• Association: Line connecting classes with multiplicity (1, 0..1, *, 1..*).
• Inheritance: Represented by an open triangle arrow symbol.
• Interface: Indicated by the «interface» stereotype.
• DCD (Design Class Diagram): Explicitly includes methods

Understanding Objects in Programming

An object is a software entity that contains data (attributes) and methods. It represents a real-world entity that can be distinctly identified.

Every object has a unique:

• Identity: The name of the object (e.g., the variable name).
• State: The data stored in the object, which defines its properties.
• Behavior: The actions an object can perform, defined by its methods.

Can an object be passed as an argument to a function?

Yes. In Python, objects are passed by reference. This means any changes made to the object's attributes within the function will permanently alter the original object. This behavior is similar to how lists and dictionaries are handled. Think of it as sharing a key to a single locker rather than getting... Continue reading "Python Classes, Objects, and Inheritance Fundamentals" »

Topic Modeling: LSI vs LDA

Latent Semantic Indexing (LSI)

Use LSI for semantic similarity, retrieval, short/sparse documents, and synonymy problems. It uses Singular Value Decomposition (SVD) to find latent concept axes from term-document co-occurrence. Concepts are mathematical directions, not clean probability-based topics. It is better when the goal is to “find similar documents.”

Latent Dirichlet Allocation (LDA)

Use LDA for discovering hidden themes and topic percentages. In this model, each document is a mixture of topics, and each topic is a distribution over words. It is better when the goal is to determine “what themes exist in this corpus?”

Key Distinction

• LSI finds latent concept dimensions.
• LDA explicitly models probabilistic topics.

1. Hardware and Spreadsheet Fundamentals

1(a) Input and Output Devices

• 1(a)(i) Output
• 1(a)(ii) Input
• 1(a)(iii) Input
• 1(a)(iv) Output
• 1(a)(v) Input

1(b) Network Types and Components

• 1(b)(i) LAN
• 1(b)(ii) MAN
• 1(b)(iii) WAN

Wireless Networking

• Component: Wireless NIC, Wi-Fi adapter
• Reason: Connects device to wireless network without cables

1(c) Spreadsheet Operations

• 1(c)(i) =C2*D2
• 1(c)(ii) Average item cost: C8; Grand total: E8
• 1(c)(iii) =AVERAGE(C2:C7)
• 1(c)(iv) Stock ID: Text; Total Value: Currency
• 1(c)(v) Dinghy, Fender

2. Data Processing and Validation

2(a) Data Entry Devices

• 2(a)(i) MICR
• 2(a)(ii) Sensor
• 2(a)(iii) OMR
• 2(a)(iv) OCR

2(b) Validation Checks

• 2(b)(i) Presence check
• 2(b)(ii) Range check
• 2(b)(iii) Format check

2(c) Database Concepts

• 2(c)(i) Boolean: Stores only