1. Advantages of Karnaugh Maps
2. SOPS And POPS
3. Properties
4. Simplification Process
5. How to solve the Karenaugh map?
6. Different Types Of K-Maps
7. Presentation Introduction
8. Don't Care Condition
9. Conclution
K map or karnaugh's map is a very important topic when studying boolean algebra.
Here is my powerpoint presentation to explain it in the easiest manner.Also I have added a question for your understanding.For the solution please write me up in the comment box.
1. Advantages of Karnaugh Maps
2. SOPS And POPS
3. Properties
4. Simplification Process
5. How to solve the Karenaugh map?
6. Different Types Of K-Maps
7. Presentation Introduction
8. Don't Care Condition
9. Conclution
K map or karnaugh's map is a very important topic when studying boolean algebra.
Here is my powerpoint presentation to explain it in the easiest manner.Also I have added a question for your understanding.For the solution please write me up in the comment box.
In electronics, an adder is a digital circuit that performs addition of numbers.
In modern computers and other kinds of processors, adders are used in the arithmetic logic unit (ALU), but also in other parts of the processor, where they are used to calculate addresses, table indices, and similar operations.
Because binary logic is used in all of today´s digital computers and devices, the cost of the circuit that implement it is important factor addressed by designers- be they computer engineers, electrical engineers, or computer scientist.
Gate level minimization for implementing combinational logic circuits are discussed here. Map method for simplifying boolean expressions are described here.
This presentation will help you to learn the basics required to learn the K map. This will help you to solve the questions related to K map. This presentation is actually the whole process of K map.
If you want to watch its video then go on https://www.youtube.com/watch?v=s3J0m7aZwGg
here I have explained the points mentioned in this presentation
In electronics, an adder is a digital circuit that performs addition of numbers.
In modern computers and other kinds of processors, adders are used in the arithmetic logic unit (ALU), but also in other parts of the processor, where they are used to calculate addresses, table indices, and similar operations.
Because binary logic is used in all of today´s digital computers and devices, the cost of the circuit that implement it is important factor addressed by designers- be they computer engineers, electrical engineers, or computer scientist.
Gate level minimization for implementing combinational logic circuits are discussed here. Map method for simplifying boolean expressions are described here.
This presentation will help you to learn the basics required to learn the K map. This will help you to solve the questions related to K map. This presentation is actually the whole process of K map.
If you want to watch its video then go on https://www.youtube.com/watch?v=s3J0m7aZwGg
here I have explained the points mentioned in this presentation
DIGITAL ELECTRONICS- Minimization Technique Karnaugh Map Trinity Dwarka
DIGITAL ELECTRONICS- Minimization Technique Karnaugh Map
4 Variable K Map
2 Variable K Map
3 Variable K Map
K-map solution for Equation
K-map for Equation
Designed to shows the animated view of working of Karnaugh map and logical simulation to the obtained minimized expression of K Map.
The coding of the project is mainly done in OpenGL and C++
167
c h a p t e r
4
Optimized Implementation of Logic
Functions
Chapter Objectives
In this chapter you will learn about:
• Synthesis of logic functions
• Analysis of logic circuits
• Techniques for deriving minimum-cost implementations of logic functions
• Graphical representation of logic functions in the form of Karnaugh maps
• Cubical representation of logic functions
• Use of CAD tools and VHDL to implement logic functions
168 C H A P T E R 4 • Optimized Implementation of Logic Functions
In Chapter 2 we showed that algebraic manipulation can be used to find the lowest-cost implementations of
logic functions. The purpose of that chapter was to introduce the basic concepts in the synthesis process.
The reader is probably convinced that it is easy to derive a straightforward realization of a logic function in
a canonical form, but it is not at all obvious how to choose and apply the theorems and properties of section
2.5 to find a minimum-cost circuit. Indeed, the algebraic manipulation is rather tedious and quite impractical
for functions of many variables.
If CAD tools are used to design logic circuits, the task of minimizing the cost of implementation does
not fall to the designer; the tools perform the necessary optimizations automatically. Even so, it is essential to
know something about this process. Most CAD tools have many features and options that are under control
of the user. To know when and how to apply these options, the user must have an understanding of what the
tools do.
In this chapter we will introduce some of the optimization techniques implemented in CAD tools and
show how these techniques can be automated. As a first step we will discuss a graphical approach, known as
the Karnaugh map, which provides a neat way to manually derive minimum-cost implementations of simple
logic functions. Although it is not suitable for implementation in CAD tools, it illustrates a number of key
concepts. We will show how both two-level and multilevel circuits can be designed. Then we will describe a
cubical representation for logic functions, which is suitable for use in CAD tools. We will also continue our
discussion of the VHDL language.
4.1 Karnaugh Map
In section 2.6 we saw that the key to finding a minimum-cost expression for a given logic
function is to reduce the number of product (or sum) terms needed in the expression, by
applying the combining property 14a (or 14b) as judiciously as possible. The Karnaugh map
approach provides a systematic way of performing this optimization. To understand how it
works, it is useful to review the algebraic approach from Chapter 2. Consider the function
f in Figure 4.1. The canonical sum-of-products expression for f consists of minterms m0,
m2, m4, m5, and m6, so that
f = x1x2x3 + x1x2x3 + x1x2x3 + x1x2x3 + x1x2x3
The combining property 14a allows us to replace two minterms that differ in the value of
only one variable with a single product term that does not include that variable a.
FYBSC IT Digital Electronics Unit II Chapter II Minterm, Maxterm and Karnaugh...Arti Parab Academics
Minterm, Maxterm and Karnaugh Maps:
Introduction, minterms and sum of minterm form, maxterm and Product
of maxterm form, Reduction technique using Karnaugh maps –
2/3/4/5/6 variable K-maps, Grouping of variables in K-maps, K-maps
for product of sum form, minimize Boolean expression using K-map
and obtain K-map from Boolean expression, Quine Mc Cluskey
Method.
Analysis & Design of Algorithms
Backtracking
N-Queens Problem
Hamiltonian circuit
Graph coloring
A presentation on unit Backtracking from the ADA subject of Engineering.
Adaptive Map for Simplifying Boolean Expressions IJCSES Journal
The complexity of implementing the Boolean functions by digital logic gates is directly related to the complexity of the Boolean algebraic expression. Although the truth table is used to represent a function, when it is expressed algebraically it appeared in many different, but equivalent, forms. Boolean expressions may be simplified by Boolean algebra. However, this procedure of minimization is awkward because it lacks specific rules to predict each succeeding step in the manipulative process. Other methods like Map methods (Karnaugh map (K-map), and map Entered Variables) are useful to implement the Boolean expression with minimal prime implicants. Or the Boolean function can be represents and design by used type N’s Multiplexers by partitioned variable(s) from the function. An adaptive map is a combined method of Boolean algebra and K-map to reduce and minimize Boolean functions involving more than three Boolean variables.
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