1. Design and hardware implementation of: 
   a. 2-bit Adder/Subtractor with XOR as well as NAND gates,
   b. 4:1 Multiplexer using universal gates and realization of Full Adder using Multiplexers,
   c. BCD Adder using two binary adders (IC based) and other gates,

Introduction: Notion of formal language. Language membership problem, why this is taken as the central problem of the subject. Finite automata and regular expressions: DFA, NFA (with and without transitions), their equivalence. Proof that FAs recognize, and regular expressions denote the same class of languages, viz., regular languages. Properties of regular languages: Pumping lemma and its use to prove non-regularity of a language, closure properties of class of regular languages, decision properties: converting among representations, testing emptiness, etc.

Probability Theory: Elementary concepts on probability – axiomatic definition of probability – conditional probability – Bayes’ theorem – random variables – standard discrete and continuous distributions – moments of random variables – moment generating functions – multivariate random variables – joint distributions of random variables – conditional and marginal distributions – conditional expectation – distributions of functions of random variables – t and χ2 distributions – Schwartz and Chebyshev inequalities – weak law of large numbers for finite variance case – central limit theorem for

Boolean Algebra, standard representation and Minimization Procedures. Logic families, combinational circuits, asynchronous and synchronous sequential circuits, Memories, PROMs AND PLAs. Introduction to VLSI systems- CMOS logic- MOS transistor theoryLayout design rules- Circuit characterization and performance estimation- Circuit simulation- Combinational and sequential circuit design- Static and dynamic CMOS gatesMemory system design- Design methodology and tools-HDL. Design of FPRG, Complex CMOS design.

Algorithmic Design Paradigms, Divide and Conquer, Analysis for Divide and Conquer, Sorting algorithms, Greedy Algorithms, Dynamic Programming, Graph Algorithms (DFS, BFS, Topological sort, Spanning Trees, All pair shortest path, Matching Max flow)

Introduction to Artificial Intelligence – Definition of AI; History and evolution of AI; Applications of AI in various domains. Problem Solving and Search Algorithms — Problem formulation, state space search, uninformed strategies (BFS, DFS), informed strategies (A*, Greedy best-first), heuristic functions, adversarial search (Minimax, Alpha-beta pruning).

Fundamentals of AC Power System: Introduction to Alternating Current – Basic concepts of AC circuits – Behavior of resistor, capacitor and inductor in AC circuits – concepts of reactance and impedance - Sinusoidal steady state analysis - Power in AC circuits. 

Three-phase systems – Basic concepts of balanced three-phase systems– Power in three-phase systems. Introduction to Electrical Machines: Basic concepts of transformers and rotating electrical machines. Diode – clipping, clamping circuits, applications in rectifiers and power supplies. 

Basic stability and device stabilization techniques (BJT). Small signal low & high frequency models for

(BJT, FET, MOSFET), Large signal amplifiers, Differential Amplifier, Instrumental amplifiers, Integrated

circuits, Tuned amplifiers, Feedback amplifiers, Oscillators, Multivibrators, Wave shaping circuits, Filter

design.

Basic stability and device stabilization techniques (BJT). Small signal low & high frequency models for

(BJT, FET, MOSFET). Large signal amplifiers - Multistage amplifiers - Differential amplifier - Tuned

• Liquid lens

• Diffraction –single slit and circular aperture

• Michelson interferometer

• Faraday optic effect

• Beam profile of a laser diode

• Fabry-Perot etalon

• Rayleigh scattering

• Diffraction – wavelength of a He-Ne laser

• Birefringence

Module 1: Exploring the subject matter of Economics

What is Economics? Definitions – Importance of Economics for Engineers – Schools of thought The Economic Problem – Scarcity and Choice – Resource allocation – the question of What to produce, How to Produce and How to Distribute Output – its nature and Importance in developing countries – Economic Systems – Basics of Capitalism, Socialism, Mixed Economy, Market Economy and Third World Economies. Is Economics a Science? Distinction between Micro and Macro Economics.

Sketching functions, Gaussian integrals, Stirling's formula, Generalised functions: Step function, Dirac delta function, properties of delta function,

Vectors and Tensors: Cartesian tensors, covariant and contravariant components of a vector, covariant and contravariant tensor, mixed tensor, metric tensor, contraction, rotations and index notation, Isotropic tensors: Kronecker delta, Levi-Civita symbol, Gram determinant. Rotations in three dimensions, Proper and improper rotations, scalars and pseudoscalars; polar and axial vectors.