Notes, summaries, assignments, exams, and exercises for Computer science for Other courses

CPU Fundamentals and Timing

Clock Cycles and Frequency

A clock that oscillates 1 million times per second (1 MHz) produces a clock cycle of 1 microsecond (1 μs), which equals 10^-6 seconds per cycle.

Instruction Execution Pipeline

The steps for executing a machine instruction are:

1. Fetch the instruction.
2. Decode the instruction.
3. Fetch the operand (if any).
4. Execute the instruction.
5. Store the result or output.

Cache Memory Operations

Cache memory is a small, fast memory used to temporarily store frequently accessed data or instructions to speed up CPU operations.

• A cache hit occurs when the CPU finds the required data in cache memory.
• A cache miss occurs when the data is not found and must be fetched from main memory.

Assembly Language Basics

General-Purpose

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

Key Concepts in Data Science & Scientific Computing

Visualization Techniques

• Overlapping Histograms: Use semi-transparent alpha parameter for comparison.

Data Structures & Algorithms

• BFS Implementation: collections.deque is ideal for Breadth-First Search.
• Grid Representation: Obstacles often represented by a value like 1.

Jupyter Notebook & Markdown

• Markdown Headings: Use # prefix for headings in Jupyter Markdown cells.

Optimization & Least Squares

• Normal Equations: Direct matrix inversion for Least Squares: β = (XᵀX)⁻¹Xᵀy.

Numerical Integration & Simulation

• Orbit Simulation: Runge–Kutta 4th order method is a common integration technique.

Search Algorithms

• Brute-Force Search: Often implemented using nested loops.

Python Ecosystem

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1. JK Flip-Flop Operation and Truth Table

Logic Diagram:

Working Principle

The JK flip-flop is an enhanced version of the gated SR flip-flop. It incorporates clock input circuitry to eliminate the invalid output condition that occurs when both S and R inputs are logic level "1".

Because of the added clock input, the JK flip-flop offers four distinct input combinations:

• Logic "1" (Set)
• Logic "0" (Reset)
• No Change
• Toggle

The S and R inputs of the preceding SR bistable are replaced by J and K inputs, named after its inventor, Jack Kilby. Thus, J = S and K = R.

The two 2-input AND gates in the gated SR bistable are replaced by two 3-input NAND gates. The third input of each NAND gate connects to the outputs Q and $\bar{Q}$. This cross-coupling allows the...

Introduction to Database Management Systems

A database is a structured collection of data stored on a computer system. It is managed using a Database Management System (DBMS), which provides the necessary tools for data storage, retrieval, and modification.

Core Benefits of Using a DBMS

• Reduced Data Redundancy: A DBMS helps minimize repeated data through organizational rules such as normalization.
• Enhanced Data Accuracy: The system uses specific rules, such as referential integrity, to maintain data consistency.
• Support for Multiple Users: Many people can access and use the database simultaneously without encountering operational problems.

Centralized vs. Distributed Databases

• Centralized: All data is stored in a single, primary location. This setup

Arithmetic Mean

The following C++ code calculates the arithmetic mean of numbers from 1 to n:

int main() {
    int n;
    double suma = 0;
    cout << "Vnesi broj: ";
    cin >> n;
    if (n <= 0) {
        cout << "Brojot na elementi mora da bide pogolem od 0!" << endl;
        return 1;  
    }
    for (int i = 1; i <= n; i++) {
        suma += i;  
    }
    double sredina = suma / n;
    cout << "Aritmetichkata sredina na broevite od 1 do " << n << " e: " << sredina << endl;
    return 0;
}

Sum

The following C++ code calculates the sum of numbers from 1 to n:

int main() {
    int n, sum = 0;
    cout << "Vnesi broj n: ";
    cin >> n;
    for (int i = 1; i <= n; i++)

Arithmetic Progressions (AP)

Sum of terms = n[(1st term + last term)]/2

Geometric Progressions (GP)

Sum of terms = [1st term(1 - quotientⁿ)/(1 - quotient)] (Swap positions of 1 & quotient if quotient > 1)

Logarithms

• log_a(x/y) = log_ax - log_ay
• log_axⁿ = nlog_ax
• log_ab = (log_cb/log_ca)

Permutations

For a set of n objects: The total number of permutations is n!

For arranging 'r' objects from a set of 'n' objects: The number of permutations is nPr = n! / (n-r)!. (e.g., ways to arrange 3 objects from a set of 5 is 5 * 4 * 3, since there are 5 possibilities for the first object, followed by 4, then 3.)

Combinations

For selecting 'r' objects from a set of 'n' objects: The number of combinations is nCr = n! / (r! * (n-r)!). (Divide by r! since there are r! ways

Sure, I'll address each of the directives.

**Q-1**

(1) **Define Symmetric Matrix:**
A symmetric matrix is a square matrix that is equal to its transpose. Mathematically, a matrix \( A \) is symmetric if \( A = A^T \), where \( A^T \) denotes the transpose of \( A \). This implies that \( a_{ij} = a_{ji} \) for all elements in the matrix.

(2) **Define Tautology:**
A tautology is a statement or formula that is always true, regardless of the truth values of its component propositions. In logical terms, a tautology is a proposition that evaluates to true in every possible interpretation.

**Reh (P.T.O)**

(3) **Write down the condition for consistency of a non-homogeneous system of linear equations:**
A non-homogeneous system of linear equations \( AX =...