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December 17th, 2014, 07:50 PM   #1
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Logic Study Guide

Hello Forum,
As I mentioned I've been working on a rather difficult problem. Specifically that I'm in the process of self-educating myself on certain topics related to math and computer science prior to starting my upcoming course in computer science, put on by my employer.

Due to the way I learn best I decided to put myself together a Simple Study Guide on Each topic as I cover them and share those resources as I create them. This "peer-to-peer" or "open source" method of learning is three-fold in that it.

1. Allows me to create a centralized repository for my own research.
2. Provides a method of potentially helping others.
3. Enables more experienced folks to critique the work and call me out when wrong so that it may be improved for all.

The method I decided to use to share this was through creating simple Markdown pages as I intend to later create a simplified wiki of sorts once the course is completed. This will allow me to link together all of pages in a logical manner (using markdown also also allows for easily creating a portable offline version of that same wiki) To that end I will post the full markdown formatted page here at the bottom of each post, but I suggest you follow the link to notehub (a site that allows you to submit md files and displays them properly for you).

Please follow this **link** to view the page with proper formatting.

Please share any criticisms, additions, or recommendations you have that you believe would make this more useful for others.

Thank you.


----------Markdown file---------------
#Logic
###Definitions

**Proposition:**

A statement that is either TRUE or FALSE.
> ex: 2+3=5 (This happens to be a true proposition)

**Predicate:**

A proposition whose truth depends on the value of variable(s).

**Truth Table:**

1. A diagram in rows and columns showing how the truth or falsity of a proposition varies with that of its components.
2. (In Electronics) A Diagram of outputs for all possible combinations of input.

**Logic Gate:**


###Overview

A Truth Table is a mathematical table used in logic to establish mathematical proof, by computing the functional values of a proposition on each of the functional arguments. That is a truth table can be used to discern whether a logical expression is true for all legitimate input values.

P and Q are boolean variables typically assigned to represent a given expression which can either be true or false, the truth of these statements can also be represented in binary using 1 for true and 0 for false (As in electronic circuitry when using high voltage to represent an on state and low voltage to represent an off state, or true and false respectively). When combined together with an operator (also known as a connective) such as "AND", "OR", or "NOT" these sentences become a "Compound Sentence" and as stated a truth table can be used to discern their logical validity.

To take this further, these logical statements can also be used in the creation of "Logic Gates" as used in electronic circuitry and computer programming.

###Operators
####Overview
There are three basic logical operators from which all others are derived, those are the NOT, the OR, and the AND. From these operators the other four basic operators are created, those gates are the XOR, NAND, NOR, and the XNOR. The rules for each of the Operators is listed below.

----
####NOT ~ (Also known as "Negation" and "Logical Inverted")
The NOT operand suggests a contradiction, in other words it takes one input in and provides an outputs with a reverse logic state.

|In|NOT Out|
|---|
|0|1|
|1|0|

----
####OR v (Also known as "Inclusive Disjunction" and "Inclusive OR" as opposed to the "Exclusive OR")
For output to be true input A and or input B must be TRUE for the output to be TRUE

|In A|In B|OR Out|
|-----|
|0|0|0|
|0|1|1|
|1|0|1|
|1|1|1|

----
####AND ^ (Also known as "Conjunction" and can be represented with the ^)
For output to be true input A AND input B must be TRUE for the output to be TRUE.

|In A|In B|AND Out|
|-----|
|0|0|0|
|0|1|0|
|1|0|0|
|1|1|1|

----
####NAND (Not AND)
A NAND Operator is simply an AND with its output inverted or "negated" as with a NOT operator.

|In A|In B|AND Out|Not Out|
|----------------|
|0|0|0|1|
|0|1|0|1|
|1|0|0|1|
|1|1|1|0|

----
####NOR (Not OR)
A NOR Operator is simply an OR with its output inverted or "negated" as with a NOT operator.

|In A|In B|OR Out|Not Out|
|----------------|
|0|0|0|1|
|0|1|1|0|
|1|0|1|0|
|1|1|1|0|

----
####XOR (Exclusive OR, also known as an "Inclusive OR" as opposed to an Exclusive OR)
An XOR acts just as an OR except it will return an output of False if both inputs are true.

|In A|In B|OR Out|Exclusive Out|
|----------------------|
|0|0|0|0|
|0|1|1|1|
|1|0|1|1|
|1|1|1|0|

----
####XNOR (Exclusive Not OR)
An XNOR acts just as a NOR except it will return an output of False if Both inputs are true (Exclusive).

Or to put it another way

An XNOR acts just as an XOR except its output will be inverted (NOT).

|In A|In B|OR Out|Not Out|Exclusive Out|
|---------------------------------|
|0|0|0|1|1|
|0|1|1|0|0|
|1|0|1|0|0|
|1|1|1|0|1|

----

###Other Resources
[Truth Table Video]()

[Logic Gate Video]()

[Truth Table Game](IXL - Truth tables (Geometry practice))

[Logic Gates in Computing](Getting Started With Digital Logic - Logic Gates)

[TruthTable Generator](Truth Table Generator)
-------------------------end file-----------------------------------------

Last edited by cynicalpsych0sis; December 17th, 2014 at 08:22 PM.
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December 18th, 2014, 12:41 AM   #2
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As long as you're motivated to continue this, I can see it being very useful for yourself and possibly many others. I had friends of mine at University that used to type up all of their physics lecture notes and convert them to PDF in order to post them online on a website and it turned out to be extremely useful to pick up on missing notes or double-check formulae/confusing things.
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December 18th, 2014, 01:06 AM   #3
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Quote:
Originally Posted by Benit13 View Post
As long as you're motivated to continue this, I can see it being very useful for yourself and possibly many others. I had friends of mine at University that used to type up all of their physics lecture notes and convert them to PDF in order to post them online on a website and it turned out to be extremely useful to pick up on missing notes or double-check formulae/confusing things.
Yeah, that's what I'm hoping for here. In fact I believe in the future this method of learning will be the predominant one. Where we don't need colleges to get a good education. If enough people continue to contribute quality research that is peer reviewed and checked, compounding this with the exponential growth of freely available information it leads me to believe the standard method for college will eventually become obsolete and the door to a quality education will open up to everyone who wants it regardless of their economic bracket.

Last edited by cynicalpsych0sis; December 18th, 2014 at 01:10 AM.
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April 18th, 2015, 11:16 PM   #4
tkk
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I am a student, and I am working with truth table now.

----------

I has been finding a truth table generator, and I have found some generator, such as:

+ http://www.brian-borowski.com/software/truth/ is good, but it requires user must have installed Java platforms on computer.
+ http://turner.faculty.swau.edu/mathe...library/truth/ is not good, because it supports only for an expression.
+ ...

I have read a similar questions, and they said that CKod (http://ckod.sourceforge.net/) is very good, but I can not use it.

I tried to do the follwing steps. But, I failed.

----------

Someone can help me to find an other truth table generator, or help me to use CKod?

Last edited by tkk; April 18th, 2015 at 11:18 PM. Reason: minor edit
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August 21st, 2015, 07:01 AM   #5
tkk
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I am a student, and I am working with truth table now.

----------

I has been finding a truth table generator, and I have found some generator, such as:

+ Truth Table Constructor is good, but it requires user must have installed Java platforms on computer.
+ http://turner.faculty.swau.edu/mathe...library/truth/ is not good, because it supports only for an expression.
+ ...

I have read a similar questions, and they said that CKen (CKen, CKen) is very good, but I can not use it.

I tried to do the following steps. But, I failed.

----------

Someone can help me to find an other truth table generator, or help me to use CKen?

Last edited by tkk; August 21st, 2015 at 07:02 AM. Reason: edit link
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August 21st, 2015, 03:40 PM   #6
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I suggest you tread cautiously when translating boolean models from the maths page to electronic circuitry, they are not always the same.
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