Homework Problems

Thread Starter

ahmadrashid17

Joined Sep 27, 2007
3
First of all, i would like to thanks for the developer of this website especially the forum section. I am new to digital logics and design. Our teacher has given homework to simplify the booleon algebric expression to specific literals; i tried alot and able to solve just one out of them. Can someone help me and solve this for me.
I am trying for last one week, though i know and learnt the laws like commutative, distributive, assosiative, but still i can not find the way to proceed. The one i solved is:

A: Simplify the expession to the said literals:

1. ABC + A'B'C + A'BC + ABC' + A'B'C' to five literals
=>ABC + ABC' + A'B'C + A'B'C' + A'BC
=>AB(C+C') + A'B'(C+C') + A'BC
=>AB(1) + A'B'(1) + A'BC
=>AB + A'B' + A'BC
=>AB + A'(B' + BC)
=>AB + A'(B' + B)(B' + C)
=>AB + A'(1)(B' + C)
=>AB + A'(B' + C) ------------- Answer

Hereby u are request to help me in question 2 to 8 which are as following:

2. BC + AC' + AB + BCD to four literals
3. [(CD)' +A]' + A + CD + AB
4. (A + C + D)(A + C + D')(A + C' + D)(A + B')

B: First take the complement and then reduce the expression to minimum literals possible:

1. (BC' + A'D)(AB' + CD')
2. B'D + A'BC' + ACD + A'BC
3. [(AB)'A][(AB)'B]
4. AB' + C'D'


I will highly appriciate your kind help. thanks
 

Thread Starter

ahmadrashid17

Joined Sep 27, 2007
3
Ok here are my try for part B:

1. [(BC' + A'D)(AB' + CD')]' i took the whole complemet
(BC' + A'D)' + (AB' + CD')'
(BC')'.(A'D)' + (AB')'.(CD')'
(B' + C)(A + D') + (A' + B)(C' + D)
B'A + B'D' + AC + CD' + A'C' + A'D + BC' + BD

Now i cant go furture can you help me....

2. [B'D + A'BC' + ACD + A'BC]'
(B'D)'(A'BC')'(ACD)'(A'BC)'
(B + D')(A + B' + C)(A' + C' + D')(A + B' + C')
Then i got hanged

3. [((AB)'A)((AB)'B)]'
((AB)'A)' + ((AB)'B)'
AB + A' + AB + B'
AB + B' +AB + B'
(A + B')(B + B') + (A + A')(A' + B)
(A + B')(1) + (1)(A' + B)
A + B' + A' + B
A + A' + B + B'
1 + 1
1


4. [AB' + C'D']'
(AB')'(C'D')'
(A' + B)(C + D)

Could some one help me in Q 1 and 2 of part B
 

Thread Starter

ahmadrashid17

Joined Sep 27, 2007
3
And for part A Q2, 3, and 4.... JUST GIVE ME A STARTING HINT for two or three steps... then i will try my self the rest
 

adn07

Joined Sep 25, 2007
16
the best soultion to your problem is to read this book :
fundamentals of logic design by Charles H.Roth,Jr.
go to chapter 2 and 3 and in chapter for you will find applications of boolean algebra ...
 

Dave

Joined Nov 17, 2003
6,960
A point about taking the compliment is that you have to take the double compliment to ensure the function remains the same. Consider the following:

- You have a function A (very simple I know)

- If you take a single compliment you end up with NOT A, which is not the same as A. You have changed the function and therefore the simplification will be different.

- If you take a double the compliment you end up with NOT NOT A, which is just A. You haven't changed the function, however you now have a compliment with which to use De-Morgans theorems.

With that in mind, have another look at your answers to section B. Also you should look at the relevant sections in the e-book for Boolean identities:

http://www.allaboutcircuits.com/vol_4/chpt_7/3.html

http://www.allaboutcircuits.com/vol_4/chpt_7/4.html

http://www.allaboutcircuits.com/vol_4/chpt_7/5.html

Dave
 
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