Axioms of Boolean Algebra

• Identity    X + 0 = X     
                  X • 1 = X

• Null         X + 1 = 1           
                 X • 0 = 0

• Idempotency:  X + X = X     
                       X • X = X

• Involution:    (X')' = X

• Complementarity:  X + X' = 1  
                             X • X' = 0

• Commutativity:  X + Y = Y + X   
                          X • Y = Y • X

• Associativity:    (X + Y) + Z = X + (Y + Z)  
                          (X • Y) • Z = X • (Y • Z)

• Distributivity:  X • (Y + Z) = (X • Y) + (X • Z)
                       X + (Y • Z) = (X + Y) • (X + Z)

• Uniting:   X • Y + X • Y' = X
                (X + Y) • (X + Y') = X

• Absorption:   X + X • Y = X 
                     X • (X + Y) = X
                    (X + Y') • Y = X • Y
                     (X • Y') + Y = X + Y

Logic Design Basic Gates

• AND – This gate is high when both its inputs are high

• OR – Gate is high when either of its inputs are high.

• XOR – Gate is high if the first or second input is high, not both.

• NOT – Gate is high when input is low.

• NAND – NOT of the AND gate.

• NOR – NOT of the OR gate.

• XNOR – NOT of the XOR gate.

GATE Computer Science Syllabus

According to official website of GATE, the syllabus for Computer Science is:

ENGINEERING MATHEMATICS    

Mathematical Logic: Propositional Logic; First Order Logic.

Probability: Conditional Probability; Mean, Median, Mode and Standard Deviation; Random Variables; Distributions; uniform, normal, exponential, Poisson, Binomial.

Set Theory & Algebra: Sets; Relations; Functions; Groups; Partial Orders; Lattice; Boolean Algebra.

Combinatorics: Permutations; Combinations; Counting; Summation; generating functions; recurrence relations; asymptotics.

Graph Theory: Connectivity; spanning trees; Cut vertices & edges; covering; matching; independent sets; Colouring; Planarity; Isomorphism.

Linear Algebra: Algebra of matrices, determinants, systems of linear equations, Eigen values and Eigen vectors.

Numerical Methods: LU decomposition for systems of linear equations; numerical solutions of non-linear algebraic equations by Secant, Bisection and Newton-Raphson Methods; Numerical integration by trapezoidal and Simpson’s rules.

Calculus: Limit, Continuity & differentiability, Mean value Theorems, Theorems of integral calculus, evaluation of definite & improper integrals, Partial derivatives, Total derivatives, maxima & minima.

COMPUTER SCIENCE AND INFORMATION TECHNOLOGY

Digital Logic: Logic functions, Minimization, Design and synthesis of combinational and sequential circuits; Number representation and computer arithmetic (fixed and floating point).

Computer Organization and Architecture: Machine instructions and addressing modes, ALU and data-path, CPU control design, Memory interface, I/O interface (Interrupt and DMA mode), Instruction pipelining, Cache and main memory, Secondary storage.

Programming and Data Structures: Programming in C; Functions, Recursion, Parameter passing, Scope, Binding; Abstract data types, Arrays, Stacks, Queues, Linked Lists, Trees, Binary search trees, Binary heaps.

Algorithms: Analysis, Asymptotic notation, Notions of space and time complexity, Worst and average case analysis; Design: Greedy approach, Dynamic programming, Divide-and-conquer; Tree and graph traversals, Connected components, Spanning trees, Shortest paths; Hashing, Sorting, Searching. Asymptotic analysis (best, worst, average cases) of time and space, upper and lower bounds, Basic concepts of complexity classes – P, NP, NP-hard, NP-complete.

Theory of Computation: Regular languages and finite automata, Context free languages and Push-down automata, Recursively enumerable sets and Turing machines, Undecidability.

Compiler Design: Lexical analysis, Parsing, Syntax directed translation, Runtime environments, Intermediate and target code generation, Basics of code optimization.

Operating System: Processes, Threads, Inter-process communication, Concurrency, Synchronization, Deadlock, CPU scheduling, Memory management and virtual memory, File systems, I/O systems, Protection and security.

Databases: ER-model, Relational model (relational algebra, tuple calculus), Database design (integrity constraints, normal forms), Query languages (SQL), File structures (sequential files, indexing, B and B+ trees), Transactions and concurrency control.

Information Systems and Software Engineering: information gathering, requirement and feasibility analysis, data flow diagrams, process specifications, input/output design, process life cycle, planning and managing the project, design, coding, testing, implementation, maintenance.

Computer Networks: ISO/OSI stack, LAN technologies (Ethernet, Token ring), Flow and error control techniques, Routing algorithms, Congestion control, TCP/UDP and sockets, IP(v4), Application layer protocols (icmp, dns, smtp, pop, ftp, http); Basic concepts of hubs, switches, gateways, and routers. Network security – basic concepts of public key and private key cryptography, digital signature, firewalls.

Web technologies: HTML, XML, basic concepts of client-server computing.

GATE Computer Science Information

Till recently, Computer Science paper was conducted in offline mode. In simple terms, it is a pen and paper based exam.

Duration:
3 hours

Exam type:
Paper-pen based. (Black point pen)

Exam pattern:
65 Objective questions.

Answering sheet: 
Optical Mark Recognition (OMR) sheets

Computer Science subject code:
CS

Qualifying marks:
25 (this varies)

Note: Scientific Calculator is allowed in the examination. An Admit card and ID card should be taken along to the exam hall.

Graduate Aptitude Test in Engineering WHAT's IT?

The GATE (Graduate Aptitude Test in Engineering) is an All-India examination conducted by seven IITs & Indian Institute of Science(IISc), Bangalore on behalf of the National Co-ordination Board, known as 'GATE BOARD' under the Dept of Education, MHRD, Govt of India. It mainly tests the comprehensive understanding of various undergraduate subjects in Engineering and Technology. 

Qualifying the GATE exam gives you an opportunity to go for Master of Technology in various good institutions in India. Recently, it has also been considered as an eligibility criteria for getting various govt. jobs in technical sectors.

GATE 2013 score is valid for TWO YEARS from the date of announcement of the GATE results. 

Benefits of Taking GATE:

• A qualified GATE score is helpful for getting admission in to IITs, IISC, IIITs, NITs and many other renowned institutions(JNTU, Anna University,DCU,Osmania University, VIT etc) in India.
• GATE qualification is also a minimum requirement to apply for various fellowships awarded by many Government organizations eg: scholarship by AICTE will be given to the candidate having a qualified GATE score when he/she pursues M.Tech.
• GATE qualified candidates are also eligible for the award of Junior Research Fellowship in CSIR Laboratories and CSIR sponsored projects.
• Many PSUs like HAL, IOCL, PGCIL, BARC etc consider GATE score
• Preparing for GATE helps in tacking various PSU level exams like COAL india, ISRO, Prasar Bharti etc.

Benefits of M. Tech:

• An M.Tech from a renowned institute gives you an edge over others.
• M. Tech opens up a lot of career paths in the fields of Teaching, Research and other Core sectors, apart from the existing alternatives
• Better Placements in top PSUs, MNCs and Indian companies both in India and Abroad.
• A Minimum stipend of 8000/- per month is given to regular students joining colleges under MHRD
• An M. Tech gives a chance to pursue specializations of interest.

Eligibility

The following categories of candidates are eligible to appear in GATE:

• Bachelor degree holders in Engineering/ Technology/ Architecture (4 years after 10+2)/Computer application and those who are in the final year of such programmes.
• Master degree holders in any branch of Science/ Mathematics/ Statistics/ Computer Applications or equivalent and those who are in the final or pre-final year of such programmes.