Combinational Logic Circuits

answer :

X (1,2,5,6)     = A/B/C/D/ + A/B/C/D + A/BC/D/ + A/BC/D
                      = A/B/C/ ( D/ + D ) + A/BC/ ( D/ + D )
                      = A/B/C/ + A/BC/
                      = A/C/ ( B/ + B )
                      = A/C/

X (3,4,15,16) = A/B/CD + A/B/CD/ + AB/CD + AB/CD/
                      = A/B/C ( D + D/ ) + AB/C ( D + D/ )
                      = A/B/C + AB/C
                      = B/C ( A/ + A )
                      = B/C

X (12,16)       = ABCD/ + AB/CD/
                      = ACD/ ( B + B/ )   
                      = ACD/

conclusion : 
 X =    A/C/    +    B/C         +     ACD/
       (1,2,5,6)     (3,4,15,16)       (12,16)

answer :
X (1,13)   = A/B/C/D/ + AB/C/D/
                = B/C/D/ ( A/ + A )
                = B/C/D/

X (3,4)     = A/B/CD + A/B/CD/
                = A/B/C ( D + D/ )
                = A/B/C

X (5,8)     = A/BC/D/ + A/BCD/
                = A/BD/ ( C/ + C )
                = A/BD/

X (15,16) = AB/CD + AB/CD/
                = AB/C ( D + D/ )
                = AB/C

conclusion :
X = B/C/D/ + A/B/C + A/BD/ +  AB/C
       (1,13)       (3,4)      (5,8)      (15,16)

answer :
X (1,2) = A/B/C/ + A/B/C
            = A/B/ ( C/ + C )
            = A/B/

X (5,7) = ABC/ + AB/C/
            = AC/ ( B + B/ )
            = AC/

conclusion :
X = A/B/ + AC/
       (1,2)   (5,7)


  
      

Boolean Algebra with DeMorgan's Theorems

     A.  (A/.B.C.)/                => A//.B/.C//

                                          A+B/+C

     B.  (A/+B/.C)/               => A//+B//.C/ 

                                          A.B+C/

     C.  (A.B(C.D)/)/            => A//.B/.C//.D//

                                          A/+B/+C+D

     D.  (A/+B/)/                  => A/ +B//

                                         A/.B

     E.  (A/.B/)/                   => A//.B//

                                         A+B

     F.   (A/+C/+D/)/            => A//+C//+D//

                                         A.C.D

     G.  (A.(B+C/)//.D)/        => A/(B/+C//)/.D/

                                         A/(B+C/).D/

                                         A/+(B.C/)+D/

     H.  ((M+N/)(M/+N))/  => (M+N/)/(M/+N)/

                                       (M/.N//)+(M//.N/)

                                       (M/.N)+(M.N/)

      I.    (((A.B)/.C)/.D)/      => A///.B///.C//.D/

                                        A///+B///+C//+D/

                                        A/+B/+C+D/

create a table of figures, cross-references, and section break

Tables of figures are used to insert the table of contents images inserted into the document. Before creating a table of figures we first insert the image that we will create the table of figures as for how to insert an image is

1. Select the Insert menu 
2. In the illustrations select picture 
3. Then select the image that we want
4. Click the insert

Once we insert the picture, hereinafter we will provide information about the image we insert it this way:

1. Select the references
2. In select insert caption captions
3. In the captions if you want to change the figure into the picture we can change it by selecting the new label and then we type the image and then click Ok

If it will automatically change the caption to the picture and then we give the description of the image as we want and then click Ok

Well if it is we now make the step table of figurenya

1. Select the references
2. In the captions we select insert table of figures
3. If it is then it will appear next to the table of figures general, we become formal formats and then click OK

Cross-reference function to insert a cross-reference both images, pages, etc..How to make it is

1. Select the Insert menu
2. In select cross-references links
3. Reference type we change according to what we want. For this time I choose an image.
4. Then on for roomates caption we select the images you want we make cross reference
5. Then insert

If you want to test its cross reference we point the cursor on the object cross reference and press ctrl + click.


section break is very helpful in arranging the layout or format of a particular section in the same document. before we set the first example of the format I want to make a section break on page 2 so place your pointer on page 2 and then we make breaknya section by:

1. Select the page layout
2. In page setup select breaks
3. Then select the section break as we want to select the next time I break

So the section break on page 2 has been created.If it lets see section breaknya chance I make a section break to separate the list on page contents and list of imagesIn the picture seen changes in the previous page table of contents is on page 1 and the list of images on page 2 now has been changed to i and ii.

circuits and logic gates equation

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Make a table of contents automatically with Microsoft Office 2007

The first thing done in weeks to create a table of contents is automatically made ​​first a book that consists of each - each such chapter, section, and sub-title.
Then after all that is done is the first step for any individual blogging - each chapter heading styles to choose one located on the menu bar home for the chapter.

Step two went on to blogging each - each section by selecting styles for sub-chapter heading 2.

and the third step blogging for each - each sub title heading styles to choose 3 for the sub title

After that create a description for each - each chapter, section, and sub-title with the title block to be made into chapters, sub-chapters, and sub ​​title by choosing multilevel list on the home menu.

If it is usually the chapter, section, and sub-title that uses Roman numerals if you want to change it we choose multilevel list => define new multilevel list => number style for this level we choose roman numerals => enter formatting for number we type Chapters I and OK.

After that we create a table of contents previous chapter I put the pointer on the left side of the title of the chapter and then Ctrl + Enter to move the chapter to the next page and previous page are used for table of contents simply by selecting the menu references => table of contents.

it will be like this

If we want to insert a chapter, section, and sub-title can do with blogging chapter title, section, or sub-title to be inserted and adjust the heading eg 2 to sub-section headings. If we have to right click on the Table of Contents that we have made select Update field will appear later Update table of contents select update entire table and then click OK then it would appear that our inserts section insert.

The last step we will create automatic numbering by choosing Insert => Page number => bottom of page and select the layout of the numbers that we want.

GOOD TRY!!!!!!!!!!