Can any one Explain Me how to Solve these Boolean Questons?

[Nipuna]

These are from my BIT notes. I think it isn't illegal to Post Here


1 reduce the following Boolean products to either 0 or a fundamental product:

a. xyx’z

b. xyzy

c. xyz’yx


2 Express E(x,y,z)=(x’+y)’+x’y in its complete sum-of-products form.



3 Let E = xy ’+ xyz’ + x’yz’. Find

a. The prime implicants of E

b. A minimal sum of E

4 Let E = xy + y’t + x’yz’ + xy’zt’. Find

a. The prime implicants of E

b. A minimal sum of E


I know the Laws but don't understand how to Apply them to those and Solve them. I didn't do math for A/L so I don't know much about them.

Sorry for Asking Stupid questions from Genius people like you Are.


Thanks

[Nipuna]

BUMP

[Neo]

Again, it is not good to submit your questions here. But I'll answer to give you a start.
Note that I can't remember all these. Please refer to your definition.

a. xyx’z

x.y.x’.z = x.x'.y.z
= 0.y.z
= 0

b. xyzy

x.y.z.y = x.y.y.z
= x.y.z

c. xyz’yx

x.y.z’.y.x = x.x.y.y.z'
= x.y.z'

2 Express E(x,y,z)=(x’+y)’+x’y in its complete sum-of-products form.

E(x,y,z) = (x’+y)’+x’y
= x . y' + x' . y this is the sum of product.

FYI:
Note that this is the function of XOR gate denoted by x ? y. See Exclusive disjunction.

3 Let E = xy ’+ xyz’ + x’yz’. Find

a. The prime implicants of E

b. A minimal sum of E

E = xy’+ xyz’ + x’yz’
= xy' + yz' (x + x')
= xy' + yz'

Prime implicants of E are xy', yz'
Minimal sum of product = xy' + yz'

(Please verify this.. I can't remember these to be honest)

[Nipuna]

Thanks You Very Much.

These are Easy than I Thought