Help me with boolean algebra!!!

This is a discussion on Help me with boolean algebra!!! within the C++ Programming forums, part of the General Programming Boards category; I have just started getting into to C++ programming and was reading the tutorial on this website. When I got ...

  1. #1
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    Help me with boolean algebra!!!

    I have just started getting into to C++ programming and was reading the tutorial on this website.
    When I got to the part about boolean algebra i got stuck
    This came straight from Wikipedia.
    Introduction to Boolean algebra - Wikipedia, the free encyclopedia
    Will someone explain this to me?


    In summary the three basic Boolean operations can be defined arithmetically as follows.
    x∧y = xy
    x∨y = x + y - xy
    ¬x = 1 - x

  2. #2
    C++まいる!Cをこわせ! Elysia's Avatar
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    x∧y = xy -> x AND y. If both x and y is 1, then the result is one; otherwise 0. As you would get by multiplying x and y.
    x∨y = x + y - xy -> x OR y. If either x or y is 1, then the result is one. If both are 0, the result is 0. Example: 1 + 1 - 1 * 1 = 1. 1 + 0 - 1 * 0 = 1.
    ¬x = 1 - x -> NOT x. That is, -x. If x is one, the result is 0 and vice versa. Example: 1 - 1: 0. 1 - 0: 1.
    Quote Originally Posted by Adak View Post
    io.h certainly IS included in some modern compilers. It is no longer part of the standard for C, but it is nevertheless, included in the very latest Pelles C versions.
    Quote Originally Posted by Salem View Post
    You mean it's included as a crutch to help ancient programmers limp along without them having to relearn too much.

    Outside of your DOS world, your header file is meaningless.

  3. #3
    The Autodidact Dante Wingates's Avatar
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    Cool

    I'll try to explain...

    "*" = "AND", + = "OR", 1 = on(true), 0 = off(false). Now imagine a circuit:
    Code:
    -----A-----
    if A is on, then the electrical current will go throught... In other words:

    1 * 0 = 0
    0 * 0 = 0
    1 * 1 = 1
    0 * 1 = 0

    or simply A * B = AB

    now imagine another kind of "circuit":
    Code:
         _A_
     ---|___|----
          B
    What happens if you turn on A "OR" B? electrical current will pass throught if one or both are on. So:

    1 + 0 = 1
    1 + 1 = 1
    0 + 0 = 0
    0 + 1 = 1

    Or simply A + B = A + B


    Then if A = 0, A * B = A(0 * ?), A + B = B(0 + ?)

    NOT(~ in C++) simply inverts.. So if A = 0, ~A = 1
    | in C++ = OR(+)
    & in C++ = AND(*)
    ^ in C++ = XOR(Exclusive OR)


    Now you should understand, I think...

    if you forget something, remember the circuit thing...

    One last example:
    Code:
             __A__
      ---A--|_____|------
               B
    It is the same as A * (A + B).

    The result should be easy to calculate, right? A * (A + B) = A

    Sorry if it is any hard to understand, but my english is not the best to explain this kind of thing... Its almost as "easy" as explain physics in another language...

    About XOR...

    1 + 1 = 0
    0 + 1 = 1
    1 + 0 = 1
    0 + 0 = 0

    The result will be 0 if both are equal, 1 otherwise
    Last edited by Dante Wingates; 06-20-2010 at 10:29 AM.

  4. #4
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    Thank you guys so much!
    I understand it now alot more

  5. #5
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    would anyone mind giving me a couple more easy problems like these?

    A. !( 1 || 0 ) ANSWER: 0
    B. !( 1 || 1 && 0 ) ANSWER: 0 (AND is evaluated before OR)
    C. !( ( 1 || 0 ) && 0 ) ANSWER: 1 (Parenthesis are useful)

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