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دانشجویان سخت افزار دانشگاه خوارزمی - تمرینات فصل 4 ساختمان گسسته

تمرینات فصل 4 ساختمان گسسته

نویسنده : دانشجو
تاریخ:جمعه 25 آذر 1390-12:39 ق.ظ

1-                          24

           18     12     8

           9        6      4

           3                2

                    1

 

2-                                                                              A=2 Inf       A=(2.4.6) => sup A=1

 

                                                                                  B=(2,9)=>sup

B=18        inf B=1

 

                                                                         C=(4.12)=> supC=12         inf C = 4

 

 

3-      اسلاید 50 دو شبکه توزیع ناپذیر است بدلیل اینکه اگر c˄  b˅d را درنظر بگیریم باید c˄b ˅ c˄d  منظور از اشتراک همان اینفیمم و اجتماع سوپریمم است .پاسخ اول c و پاسخ دوم d  می شود پس شبکه خاصیت توزیع پذیری ندارد .

 

4-                                                       

0

1

1

1

                              جواب ’x+    yاست

5-      M0=a+b

M1=a+b’

M2=a’+b

M3=a’+b’

Ab’=01====< (a+b’)( a+b)(a’+b )  =

m0+m2+m3

 

 

 

6-      زیرا برای d.e سوپریمم وبرای b,c اینفیمم وجود ندارد.

 

 

7-      شبکه d28 رادر نظر  میگیریم زمانیکه خطوط را به هم وصل می کنیم بصورت یال یک یال نیز از 2به 14 ارتباط می دهیم در نتیجه سوپریمم ان 28 و اینفیمم 1 نمی شود زیرا برای دوعدد سوپریمم همان عدد بالا 14 و اینفیمم 2 می باشد. در حالیکه وقتی شبکه جبر بول است که برای  تمامی عناصر یک متمم منحصر به فرد وجود داشته باشد و علاوه بران محدود باشد وتوزیع پذیر . و خاصیت متمم در شبکه آن بود که هر دوعنصر در شبکه که متمم هستند فقط دارای یک سوپریمم و اینفیمم باشند . در d28  تمام عناصر باید دارای سوپریمم 28 و اینفیمم 1 باشد که نیست پس شبکه جبربول نمی باشد.                             28

                              14           4

                               7            2

                                      1

8-       شرط لازم و کافی برای اینکه a<b اینست که aحتما زیرمجموعه b  باشد .

 

 

9-                 0   1                                1   1                       1   0                                0   0

X’yz’

X’yz

X’y’z

X’y’z’

Xyz’

xyz

Xy’z

Xy’z’

             

                           X+x’(y’z’+yz’) بصورت dnf باید تمام جملات بصورت ضرب xyz در اید تا بتوان ساده کرد و درجدول کارنو نوشت . البته در جدول کارنو بصورت بالا نوشته نمی شود فقط در جدول جای چند جمله ای با یک نشان داده می شود برای سهولت درک مطلب بصورت فوق نوشته شده است . جمله x  را یکبار در y’z’ و یکبار در yz’ و همینطور x’ را به همین شکل در پرانتز ضرب کرده که بصورت زیر بدست می آید xy’z’+xyz’+x’y’z’+x’yz’                         

زمانی که در جدول کارنو قرار می دهیم پاسخ فقط z’   حاصل می شود .

 

10-  عبارت بعدی نیز به شکل بالا باید با ضرب به صورت چند جمله ای های یکسان دراید سسپس پاسخ نهائی y می شود

 

11-  شبکه کراندار که حداقل یک عضو متمم نداشته باشد می  توان به d28 درمثال بالا اشاره کرد .



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