December 17th, 2014, 08:50 PM  #1 
Newbie Joined: Dec 2014 From: home Posts: 7 Thanks: 0  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 selfeducating 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 "peertopeer" or "open source" method of learning is threefold 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. InNOT Out  01 10  ####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 AIn BOR Out  000 011 101 111  ####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 AIn BAND Out  000 010 100 111  ####NAND (Not AND) A NAND Operator is simply an AND with its output inverted or "negated" as with a NOT operator. In AIn BAND OutNot Out  0001 0101 1001 1110  ####NOR (Not OR) A NOR Operator is simply an OR with its output inverted or "negated" as with a NOT operator. In AIn BOR OutNot Out  0001 0110 1010 1110  ####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 AIn BOR OutExclusive Out  0000 0111 1011 1110  ####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 AIn BOR OutNot OutExclusive Out  00011 01100 10100 11101  ###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 09:22 PM. 
December 18th, 2014, 01:41 AM  #2 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,084 Thanks: 699 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
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 doublecheck formulae/confusing things.

December 18th, 2014, 02:06 AM  #3  
Newbie Joined: Dec 2014 From: home Posts: 7 Thanks: 0  Quote:
Last edited by cynicalpsych0sis; December 18th, 2014 at 02:10 AM.  
April 19th, 2015, 12:16 AM  #4 
Newbie Joined: Apr 2015 From: Japan Posts: 3 Thanks: 0 
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.brianborowski.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 19th, 2015 at 12:18 AM. Reason: minor edit 
August 21st, 2015, 08:01 AM  #5 
Newbie Joined: Apr 2015 From: Japan Posts: 3 Thanks: 0 
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 08:02 AM. Reason: edit link 
August 21st, 2015, 04:40 PM  #6 
Senior Member Joined: Jun 2015 From: England Posts: 716 Thanks: 203 
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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