Course module

CS | 01 | Digital Logic and Circuits and Discrete Mathematical Structures — UP LT Grade Assistant Teacher 2025 Computer Science Course

Lessons: 423
Duration: 45 hr 39 min
PYQs: 311
Practice: 2209

7% of this course's PYQ weight is covered in this module.

Syllabus index

Lessons in this module

423 linked lessons

Digital Systems & Boolean Basics

Digital Fundamentals & Boolean Algebra

Lessons

UPLT - Topic Wise Test - Digital Logic and Circuits and Discrete Mathematical Structures - Digital System & Boolean BasicsTest

Number System

Basics & Decimal Convert

General Base Conversion

Binary, Octal & Hex

Base 2 Conversion DirectlyDrm Video

Lessons

UPLT - Topic Wise Test - Digital Logic and Circuits and Discrete Mathematical Structures - Number SystemTest

Number Representation

Basics to 1s Complement

2s Complement & Math

BCD & Special Codes

Lessons

UPLT - Topic Wise Test - Digital Logic and Circuits and Discrete Mathematical Structures - Number representationTest

Logic Gates & Hardware

Evolution, NOT, OR & AND Gates

Universal Gates: NAND & NOR

Ex-OR, Ex-NOR Gate & Relation

Lessons

UPLT - Topic Wise Test - Digital Logic and Circuits and Discrete Mathematical Structures - Logic Gates & HardwareTest

Boolean Expression

SOP & POS Canonical Forms

Boolean Function Counts

Functional Completeness

Universal Realization

Lessons

UPLT - Topic Wise Test - Digital Logic and Circuits and Discrete Mathematical Structures - Boolean ExpressionTest

Boolean Minimization

K-Map Structure & PIs

Logic Circuit Analysis

Adv. Laws & Optimization

Lessons

UPLT - Topic Wise Test - Digital Logic and Circuits and Discrete Mathematical Structures - Boolean MinimizationTest

Combinational Circuit

Adders & Subtractors

CLA & Arithmetic Logic

Multiplexers (MUX)

DeMux, Decoder & Encoder

Hazards & Timing

Lessons

UPLT - Topic Wise Test - Digital Logic and Circuits and Discrete Mathematical Structures - Combinational CircuitTest

Sequential Circuits

Seq. Logic & Latches

Flip-Flops & Conversion

Sync Counter Analysis

Sync Counter Design

Ripple (Async) Counters

Shift Registers

Ring & Johnson Counters

Lessons

UPLT - Topic Wise Test - Digital Logic and Circuits and Discrete Mathematical Structures - Sequential CircuitTest

Set Theory

Sets, Representation of Sets and Hierarchy of numbers

Finite, Infinite, Countable, and Uncountable Sets

Null, Universal, Subsets, Proper Subsets

Power Set and its Cardinality

Set Operations – Union, Intersection, Set Difference, Symmetric Difference, and Complement

Lessons

UPLT - Topic Wise Test - Digital Logic and Circuits and Discrete Mathematical Structures - Set TheorryTest

Relations

Cartesian Product, Relation, Inverse & Complement

Reflexive Irreflexive Relation – Count, and Properties

Symmetric Anti-Symmetric Asymmetric Relation and Properties

Transitive Relation – Definition, Count, and Properties

Partial Order Relation – Properties, Partially Ordered Set (Poset), and Total Order Relation

Lessons

UPLT - Topic Wise Test - Digital Logic and Circuits and Discrete Mathematical Structures - RelationsTest

Functions

Definition of a Function – Domain, Co-domain, Range, and Count of Possible Functions

Composition of Functions – Definition, Properties, and Examples

One-to-One (Injective) Function – Definition, Count, and Properties

Onto (Surjective) Function – Definition, Count, and Properties

Bijective Function – Definition, Count, and Properties

Inverse of a Function – Definition, Existence Conditions, and Examples

Lessons

UPLT - Topic Wise Test - Digital Logic and Circuits and Discrete Mathematical Structures - FunctionsTest

Graph Theory

Introduction to Graphs – Definitions, Terminology (Loops, Parallel Edges, Adjacent Vertices)

Types of Graphs – Finite, Infinite, Null, Trivial, Complete

Bipartite, Cycle, Regular, and Complement of a Graph

Degree of Vertex – Isolated and Pendant Vertices, Handshaking Lemma, and Degree Sequence

Minimum and Maximum Degree – Relationships, Degree Constraints, and Havel-Hakimi Theorem

Graph Traversal – Walk, Path, Trail, Circuit, and Connected Graphs

Euler and Hamiltonian Graphs – Definitions, Conditions, and Examples

Planar Graphs – Kuratowski’s Theorems, Homorphism and examples

Euler Formula – Planar Graph Formula, Applications, and Derived Relations

Graph Coloring – Vertex Coloring, Edge Coloring, Chromatic Number, and Coloring Theorems

Trees – Definitions, Properties, Eccentricity, Diameter, Radius, and Center

Spanning Tree and Spanning Forest – Definition, Construction, and Applications

Cut Set and Connectivity – Edge Connectivity, Vertex Connectivity, and Cut Set Concepts

Lessons

UPLT - Topic Wise Test - Digital Logic and Circuits and Discrete Mathematical Structures - Graph TheoryTest

Group Theory

Closure-Algebraic Structure, Associative-SemiGroup, Identity-Monoid

Inverse Property and Group

Commutative Property and Abelian Groups

Classification of Finite and Infinite Groups

Lessons

UPLT - Topic Wise Test - Digital Logic and Circuits and Discrete Mathematical Structures - Group TheoryTest

Propositional and Predicate Logic

Introduction to Propositions, Laws of Contradiction and Excluded Middle

Types of Propositions – Atomic and Compound

Logical Operators – Negation, Conjunction, and Disjunction

Implication and Bi-Conditional Operators in Logic

Types of Logical Cases – Tautology, Contradiction, Contingency, Satisfiability, and Validity

Introduction to First Order Predicate Logic

Quantifiers – Universal and Existential

Lessons

UPLT - Topic Wise Test - Digital Logic and Circuits and Discrete Mathematical Structures - Propositional and Predicate logicTest

Permutation and Combination

Basic Concepts & Counting Principles

Permutations (with & without Repetition)

Circular & Grouping Permutations

Combinations (with & without Repetition)

Special Applied Problems

Advanced Counting Theorems

Module lessons

Lessons

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