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Boolean Algebra Lesson: Lesson sites and publications addressing

Recommendations for further study

reference books:

• Enrico Ambrosini, digital electronics, Tramontana 2005
• Assunta Martino, Advanced Electronics with PSpice A / D Windows, Calderini
• Riffoldi Gabriel, Course of Electronics and Telecommunications Electronics - Digital 1, Etas

Referring Sites:

• seen by the Digital Electronics wikipedia
  
• Tutorial for instrumentation and equipment for the laboratory
  
• Electronics to start
• Oddities and Curiosities to enjoy studying
  
• collection of links of Electronics (to see!)
  

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Boolean algebra: Boolean algebra Check

review exercise

1. Give the definition of Boolean algebra.
2. The logic AND-OR-NOT, for each of them draw the circuit symbol and describe it.
3. Write and briefly explain the associative property and the theorem of De Morgan.
4. Using Boolean algebra, to minimize the following logical expressions:

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Lesson: Lesson Lab

laboratory experience

Given the following circuit, obtain and verify the truth table. The gate shown is a two-input NAND gate (combination of an AND gate and a NOT connected in cascade).
Tools and materials required:

• stabilized power supply;
• IC 7400 (or IC 4011), two 1 Ohm resistors, a 100 Ohm resistor, an LED;
• Bread-board.

diagram




Steps:

• Circuit realization;
• Calibration adapter and connection to the circuit
• Experimental verification of the truth table .

Realizing, for this brief experience, an elaborate form of a report.

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algebra: Properties and theorems (2 / 2) Boolean Algebra

Main Properties and theorems

Duality
If a logical expression is true, that satisfies the axioms of Boolean algebra, its dual is also true.
In fact, the first column of the Boolean axioms can be replaced in the second if you swap the AND operator with the OR operator, each one with a 0 and each 0 with a 1 and vice versa, you can go to the first and second columns. This property is called duality and is valid for any logical expression true.

Property Please note the following link for further information. Properties of Boolean algebra.


Theorems

Please note the following link for further information. theorems of Boolean algebra.

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Lesson: Properties and theorems (1 / 2) Lesson

Summary and clarification ...

The Boolean algebra is based on the following axioms: Operator (·) is called the operator of logical product (AND).
The operator (+) operator is called the logical sum (OR).
The operator (¯) is called a logical operator (NOT).
These axioms must be accepted in Boolean logic and therefore should not be interpreted according to mathematical rules and usual (in this case would be absurd to put 1 + 1 = 1).
circuit interpretation of these axioms can be given through the following illustration:

quest'algebra Exploiting the rules can be expressed in summary form, the logic function of any circuit, through its logical expression . For example the expression:

satisfies the truth table:

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algebra: Some Examples

Examples

With simple examples one can easily understand how Boolean algebra is also in our daily lives.

eg 1: "I go out if weather is warm AND " - ---------->

<--- Es. 2 :"esco se è bel tempo OR if it is hot "

Example 3: "I go out if weather is warm AND OR commitment." --->





Please note the links for further information. Principles of 'Boole's algebra

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Boolean Algebra Lesson: Negative logic Boolean algebra

Negative logic - NOT

The NOT is reduced to a simple negation of the value acquired.

Symbol and property

Logic function

Please note the following link for further information. Negative logic

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Lesson: Sum logic Boolean algebra

Sum logic - OR

The RO instead returns true if and only if at least one of the two values \u200b\u200bis true, in a nutshell in several successive operations OR if only one value is true and the result will be.

Symbol and property

Logic function

Please note the following link for further information. logical sum

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Lesson: Product

logical product - AND

We can easy to understand that the AND returns true if and only if the other two values \u200b\u200bare true, this means that even in a succession of further operations AND if only one value is false and the result will be. In digital circuits, the AND gate is a mechanism common to have a true signal if a god ro other signals are all true.

Symbol and property

Logic function


Please note the following link for further information. Product logical

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logical Boolean Algebra Lesson: Basic Algebra Lesson

Basics

L ' Boolean algebra is defined on a finite set of values \u200b\u200b(the two values \u200b\u200b true and false ) that you can manipulate through appropriately defined functions. These functions operate on one or two Boolean variables, and produce results in a single value, which is also boolean.

In dealing with Boolean algebra, we must bear in mind that the logic and not in a numbering system, logic works, in fact, with only two values: 0 and 1 (not intended as numbers!). The logical variables are generally indicated by capital letters A, B, C, ... The operands are the main three: denial or NOT (¯, or!) or logical sum OR (+); product AND logical or (x).

Please note the following link for further information. Boolean algebra.

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Boole: A bit of history

Brief historical note

George Boole created the conceptual tool that is fundamental to the functioning of the computer and that, in his honor, goes by the name of 'Boolean algebra'. This is a two-valued logical calculus of truth with some particular laws, which allows you to operate the same way that propositions about mathematical entities. He described the logical operators that he took the name of: Boolean operators.

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Boole's algebra lesson: Lesson of Electronics

Introduction: Internet

sure everyone uses the Internet for many hours a day, and in particular search engines.

" Try to find web pages that speak of the relationship between mouse and Disney. We do not want pages that talk about mouse without mentioning Disney or pages that talk about without mentioning Disney mouse, but only pages that talk about both. Our research requires the operator AND : Disney AND mouse. However, if we wanted to find all pages that talk about Disney - even though there is talk of mouse - and with all the pages that discuss mouse - even if Disney is not mentioned - we did a search in OR : Disney OR mouse. Finally NOT : its use is fairly intuitive: the search for mouse AND (NOT Disney ) gives us such as all pages that discuss mouse, and which is not mentioned Disney "

" In everyday life, we think For example, when we want to leave the house if it rains we can not get out, this thought process, that is the test if it rains, it can take two states, or is it true (and therefore do not go out) or is false (and then we go out). One can understand that if this kind of logic is useful to us as human beings, it is even more for a computer because its language is made of bits and you can only associate with the true value 1 and the false value 0. "

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Internet: index of lesson

Happy Lesson

This lesson is structured as follows :

• Introduction and historical notes
• Basics
• AND - logical product
• OR - logical sum
• NOT - denial
• Examples
• Theorems and properties
  
• Laboratory

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lesson Electronics: Target

Prerequisites to the lesson and objectives

As a prerequisite to this lesson on algebra of Boole Occor that ' students learn the principles basic logic gates and the most important key concepts of binary systems. Along with the aforementioned arguments, with arguments that it is, the student will have the foundation needed to address any digital electronics class that during the third year will be addressed. In addition will serve as a basis for understanding the arguments of the subsequent years to maturity.

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lesson Electronics: Period Time and Electronics

period and time to carry out the lesson

This lesson is planned for the first part of the school year. Indication must be held after the introduction different numbering systems, in particular the binary numbering system, insiame to the main gates. The lecture topic is expected to be four hours, two lessons of two hours each. Next to the theory there will be another six hours and includes: two hours for exercise and curiosity more than four hours for the laboratory to practice what they learn theoretically.

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Lesson: Level

level of the lesson

The lesson on algebra of Boole serves to introduce the basic concepts of digital electronics useful for a course of study but also to inidizzo Electronic Computer. The Boolean algebra is introduced in a larger teaching unit which will introduce the basic concepts of logic gates and their basic properties.

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lesson lesson Electronics: Title

algebra

This lesson is aimed at students in third-Technical Institute that after two years, beginning their course of study to address. In this case the address can be Information Technology or Electronics. The argument in question is part of the 'teaching of electronics.

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FIUMICINO, 06/11/2008

Finally I went for the first time at the Rome meeting of the Carp Team ... I have found since the restaurant a very friendly atmosphere and little confidence from the members .. (It must have been the wine)??

I do not know but I know most of the team and also President of which I was welcomed with applause ... (THANKS DEAN ')

Right away I felt comfortable xke' are admirable people who love what they and are struggling to do so in the best way ..

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I hope that the PIRATE nn yesterday is proof of what I can stand up .... I know that eating fish boilies ... I did "hear" a couple of performance I burned the hairs in the nose (the bomb cernobill ..??? and nothing in comparison) ... However I can say that I'm willing to give my 100% availability and to cooperate with them if you need Startup .... thanks RCT

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FISHING ..... Favalanciata ....


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loads as pack mules, we left for this trip in the nature ..... Here we go ...........

CARINI E '?!..................

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I met a crazier than me .... his "crew" of ideas and valuable advice and too big ... is helping me to get a view of everything ... we met only once, and I repeat once ... casserole dish, but ... and then say 'a big ..
think the only time we met I was not able to hold a carp in hand (I said slipping) as n idiot ... and 'a fish that slips some idiot ....
short, I was close to his spot where there was the girl's sister and ilaria sergio another crazy from what I understand ..
at some point my rods begin to play ...... "Casserole dish BUT I THINK SO MY"
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FAIR RESULT FROM A BEAUTIFUL BELLE 6 kg .....

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as a child I followed him and tried to understand the technical secrets and everything there was to know about this wonderful sport (passion) or as a hobby you like to call ...

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