Boolean Algebra Notions: 07/12/01

by Fred J. Schaal


This lesson was created as a part of the SMART website and is hosted by the Illinois Institute of Technology

The purpose of this web page is to introduce some fundamental Boolean Algebra ideas.

                    These notions are pretty different, so suspend all judgment until you have mastered the basics.  Take this stuff on faith.  Look up Mr. < a href="http://www.kerryr.net/pioneers/boole.htm"> Boole on the internet for details of his fascinating life and times.

                    The Boolean operations that I shall deal with are and--L and or--V.  There are other symbols for these operations but they are to be avoided.  (Confusion lies is their wake.)    

                    I want to set up the truth table for and--L and the truth table for or--V.

A

B

ALB

AVB
T T T T
F T F T
T F F T
F F F F

                        The variables in Boolean, here A and B, take only two values.  I use T and F, standing for true and false,  but others use 1 and 0, red and green, on and off, in and out, etc.  The idea is to have two easily distinguishable values.  Under A I  blink the variable thru its possible values: T, F, T, F.  Under B I stutter blink the variable thru its possible values: T, T, F, F.  For the case of just two variables there are just  four cases to handle all possible combinations of the values of the variables: T T, F T, T F, F F. Think about this!.

                    Knock, Knock. 

                    Who's there? 

                    Boo.  

                    Boo who? 

                   BOO BOO BOOLEAN!

 

                 T and T is T but all the rest are F.  T  or T is T and only F or F is F.  L likes to be F.  Therefore any F will make L F.  V likes to be T and any T will make it T.  The only time that V is F is when both A and B are F.

                A third thing I need is negation.  Not A and Not B.  Some people use the tilde before the variable to indicate negation  ~A, but I prefer to use a bar over the variable to indicate negation.  e.g. A¯.  Unfortunately I cannot get the bar to appear  over the variable.  So I shall be content to have it  lag a snidge behind the negated variable.  Below is a table of two variables and their negations:                                                 

A

B

T T F F
F T T F
T F F T
F F T T

                

                 Now  I shall create the opportunity for you to and and to or a variable with its negation.  

A AL AV
T F

F T

                    To do these fill ins just look at the table for   and and or.  Recall that and likes to be false and or likes to be true.                    

                    How about doing  A and  B¯ and  A¯ or B?  I'll even let you fill in the columns for B and the negated variables not A and not B.  Refer to the above truth table for negation and to the previous truth table for  and and or.  Be sure to stutter blink  the values of the B variable.

 

A B A¯    ALB¯ VB
T




F




T




F




                    Print these pages and fill in the missing entries in the above tables.  Highlight the important ideas is the text. Use the approved color scheme for these highlights.  Return these pages to me in a  sealed envelope.  Put my name, your name and period, the date, and the name of this web page on the envelope.

                    Once you have filled in the tables you may cheer  

in the words of George W....

                      BOOLA BOOLA, BOOLA BOOLA etc.  

                    An after thought about the color coding used on this web page: AND  is yellow, OR is cyan, NOT A is red and NOT B is green.


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