HDLC and PPP Data Link Protocols Explained

HDLC Frame Control Fields

The Information (I) field is used to transport user data and network layer data. It includes information for error and flow control (where piggybacking is applicable).

It contains a 1-bit Poll/Final (P/F) bit (if it’s 0, it’s an I-frame) and the next 3 bits: N(S) (send sequence number) and the last 3 bits: N(R) (receive sequence number), which is the acknowledgment field when piggybacking is used.

The N(S) and N(R) bits are only meaningful when the P/F bit is active. The P/

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Calculus Proofs: Continuity, Derivatives, and Limits

1. Let f and g be continuous functions from D to R. Prove that f + g is continuous on D using the definition of continuity.

Proof: We must show that f + g is continuous at c for each c ∈ D. Let c ∈ D and ε > 0. Since f is continuous at c, there exists a δ₁ > 0 such that if x ∈ D and |x – c| < δ₁, then |f(x) – f(c)| < ε/2. By the continuity of g at c, there exists a δ₂ > 0 such that if x ∈ D and |x – c| < δ₂, then |g(x) – g(c)| < ε/2. Let δ = min{δ₁,

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Business Statistics and Data Analysis for Managerial Decisions

Statistics and Business Analytics: Definitions, Needs, and Importance

Statistics is the science of collecting, organizing, analyzing, interpreting, and presenting data. It helps in converting raw data into meaningful information for decision-making.

Business Analytics refers to the use of statistical methods, data analysis, predictive modeling, and fact-based management to drive business planning. It focuses on turning data into actionable insights to solve business problems and improve performance.

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Discrete Mathematics & Probability Essentials

Probability Fundamentals

Probability is defined as the ratio of the number of successful outcomes to the total number of possible outcomes. Every probability problem involves a probability space, which consists of:

  • Sample Space: A non-empty, countable set containing all possible outcomes of an experiment.
  • Probability Function: A function that maps each outcome to its probability. The sum of probabilities for all outcomes in the sample space must equal 1.

Core Probability Rules

Complement Rule

P(not A)

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Geometry Problems: Circles, Chords, and Quadrilaterals

Geometry Problems and Solutions

Here are the solutions to the geometry questions:

  1. Cyclic Quadrilateral Angle Sum

    Question: The sum of either pair of opposite angles of a cyclic quadrilateral is 180°. If ‘n’ represents this sum and ‘m’ is also 180°, find ‘m-n’.

    Solution: In a cyclic quadrilateral, the sum of opposite angles is always 180°. Therefore, \(n = 180^\circ\). Given \(m = 180^\circ\), we have:

    \[m – n = 180^\circ – 180^\circ = 0\]

  2. Circle’s Largest Chord and Radius

    Question: If the largest chord

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Essential Math Formulas and Definitions

Lines

Slope-Intercept Form

y = mx + b

Point-Slope Form

y – y₁ = m(x – x₁)

Standard Form

Ax + By = C

Rate of Change (Slope)

Δy/Δx = (y₁ – y₂)/(x₁ – x₂)

Algebra Formulas

Quadratic Equations

Standard Form

ax² + bx + c = 0

Quadratic Formula

x = [-b ± √(b² – 4ac)] / (2a)

Binomial Expansions

(a + b)³ Expansion

a³ + 3a²b + 3ab² + b³

(a – b)³ Expansion

a³ – 3a²b + 3ab² – b³

(a + b)² Expansion

a² + 2ab + b²

(a – b)² Expansion

a² – 2ab + b²

Exponent Rules

Product Rule

xᵃ ·

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