While appearing in the GATE ECE exam, Minimization MCQ questions constitute an important part of the paper. As they test the candidate on the parameters of critical thinking and problem solving, these skills also come in handy while appearing in other exams that are designed to evaluate the understanding of STEM concepts of an applicant, such as NIELIT, SSC JE, and the kind.
Minimization in digital logic and boolean algebra refers to the process of simplifying and breaking down complex algebraic expressions into their most rudimentary terms. It plays an important role in the analysis of logical circuits, for it serves to reduce complex combination logical circuits without interrupting the basic function of the circuit. Consequently, a firm grasp over minimization becomes a prerequisite for anyone wishing to appear on the GATE ECE paper.
Important Minimization topics for GATE ECE
Given below are the minimization topics for GATE ECE that a candidate is expected to cover while covering the minimization GATE syllabus and while taking minimization quiz.
It is a field of engineering in which the representation of all the different constituent sequences and signals of a digital circuit is achieved with numbers. Mostly finding usage in electronic devices, the importance of digital logic makes minimization for computer science an important field of study. Broadly, there are two kinds of digital logic circuits- combinational and sequential.
In the field of mathematics and logic, a boolean function refers to a function of which the arguments and the function itself derive their values from a set comprising two values. For this reason, boolean functions are also termed as switching functions. If in a boolean function, the number of variables or entries is n, then the number of all possible combinations of the variables will always amount to be 2n.
Sum of Products (SOP)
Sum of Products refers to a type of Boolean algebra expression that consists of the addition of the different product inputs. The products of these inputs in Boolean logical AND while the addition is Boolean logical OR.
Product of Sums (POS)
Product of Sums refers to a type of Boolean algebra expression which consists of sums comprising single or multiple variables that might be present either in their true normal form or in their complemented form or even as combinations of both.
The Karnaugh map is a graphical method and technique of solving logical expressions and simplifying Boolean expressions. K-maps use truth tables to provide us with a more straightforward form of a complicated logical expression.
Tips to solve minimization questions for GATE ECE:
Listed below are a set of tips and tricks that can prove extremely beneficial for students while solving minimization for computer science and ECE in GATE and other technical examinations.
- At the outset, be very fluent with the various rules associated with the simplification of boolean algebra, such as DeMorgan’s Law, Complement Law, Commutative Law, and the like.
- Be thorough with the various steps involved while simplifying or reducing an expression with the help of a K-Map.
- One must keep the order of Boolean Algebra operations in mind before proceeding with their simplification and subsequent evaluation. They are the same as standard algebra.
- Always have the schematic representation of the circuit in place when you are attempting to simplify the Boolean expression on consideration.
Importance of minimization in GATE
The following points shed light on the importance of minimization in the GATE and other similar entrance examinations.
- It is an important tool for candidates to visualize and comprehend complex combinatorial circuits.
- It helps you evaluate complicated network analysis problem statements rather conveniently, helping you save valuable time in the process.
- It reduces the inherent complexity, and the cost of the associated circuit for the minimized version of the Boolean expression always has a lesser number of logic gates than the original circuit.
- Familiarity with the concepts of minimization helps a candidate tackle problems both in GATE ECE as well GATE CSE as the field of digital design witnesses an overlap in both of these disciplines.
Most recommended books for minimization for GATE
The following minimization books are among the ones that are most recommended to students who are attempting a minimization online test or a minimization online quiz. They comprehensively cover all the topics included in the minimization syllabus for GATE and act as the perfect resource for compiling minimization GATE notes as well as minimization notes for ECE.
Digital Logic and Computer Design
M. Morris Mano
Digital Circuits and Design
S Salivahanan and S Arivazhagan
Fundamentals of Electric Circuits
Charles K. Alexander, Matthew N.O. Sadiku
Signals and Systems
Oppenheim Alan V, Willsky Alan S, Nawab S. Hamid
Why prepare minimization for BYJU'S Exam Prep?
Gradeup’s comprehensive bank of minimization notes for GATE pdf coupled with its minimization gate questions and answers PDF helps candidates gain an in-depth understanding of all the various concepts that are entailed under this particular topic. Irrespective of whether a candidate is looking for minimization notes for gate ECE, Mechanical, Civil, Electrical, and CSE or minimization study material for gate ECE and all the various branches, BYJU'S Exam Prep acts as a one-stop solution for them and furnishes them with additional practice material with its minimization MCQ pdf.
Ques. How can logic gates be reduced?
Answer: The first step in reducing a logic circuit involves writing the Boolean equation for the logic circuit
Ques. What does Boolean logic use?
Answer: It accepts all values in either True or False
Q. What is DeMorgan’s Theorem?
Answer: DeMorgan’s Theorem has two postulates:
- The complement of a product term is equal to the sum of the complements.
- The complement of a sum term is equal to the product of the complements.
Q. What is a totem pole output?
Answer: It is a standard output of a TTL gate that is designed to reduce the propagation delay in the circuit
Q. What are Don’t Care terms?
Answer: The output levels that are not defined owing to non-occurring input conditions are referred to as Don’t Care terms.