# logic circuits equations

Discussion in 'Homework Help' started by SHuzero, Aug 9, 2011.

1. ### SHuzero Thread Starter New Member

Feb 22, 2011
14
0
can you help me to simplify this equation (x'y'+z)'+z+xy+wz ? please help me to simplify that equation.

also what is the essential prime implicants in this equation f(w,x,y,z)=summation of m(0,2,4,5,6,7,8,10,13,15)?

kindly help me with this problems.....

2. ### Zazoo Member

Jul 27, 2011
114
43
Hello,
Can you show us your attempt at a solution for each problem?

3. ### Anestis88 New Member

Aug 9, 2011
19
2
The equation is simplified as :

(x'y'+z)'+z+xy because z+wz=z
(x'y')'*z'+z +xy
(x+y)*z'+z +xy
(x+y+z)(z+z')+xy because x+yz=(x+y)(x+z)
x+y+z+xy
so x+y+z

4. ### SHuzero Thread Starter New Member

Feb 22, 2011
14
0
guys help me
what is the essential prime implicants in this equation f(w,x,y,z)=summation of m(0,2,4,5,6,7,8,10,13,15)?

I wanted to know what is the essential prime implicants in this equation when it is in k-map

kindly help me with this problems.....

5. ### SHuzero Thread Starter New Member

Feb 22, 2011
14
0
hello guys
(x+y)*z'+z +xy
(x+y+z)(z+z')+xy because x+yz=(x+y)(x+z)

how come this part
(x+y)*z'+z
have been reduced to this
(x+y)*z'+z
(x+y+z)(z+z') because x+yz=(x+y)(x+z) - where is this equation....i can't see it....
i need some explanation

6. ### SHuzero Thread Starter New Member

Feb 22, 2011
14
0
this is my solution to essential prime implicants is

f= w'z'(y+y')(x+x') + xz(w'+w)(y+y') + wx'z' (y+y')
f= w'z' + x'z + wx'z'

I just short cut my solution because it can be seen in k-map...

what it the essential prime implicant

7. ### Anestis88 New Member

Aug 9, 2011
19
2
A+B*C=(A+B)(A+C)

so in the (x+y)*z'+z
if A=z , B=z' and C=x+y
A+B*C=(A+B)(A+C)
z+z'(x+y)=(z+z')[z+(x+y)]