# Boolean equations

#### kallen

Joined Jun 2, 2004
1
I am so confused, can someone pleaase help?

Prove the identity of each of the following Boolean equations, using algebraic manipulation:

a) AB + B C' D' + A' B C + C' D = B + C' D

B) WY + W' Y Z' + WXZ + W' X Y' = WY + W' X Z' + X' Y Z' + X Y' Z

c) A C' + A' B + B' C + D' = (A' + B' + C' + D')(A + B + C + D')

Thanks so much!!!!!

#### susi

Joined Jun 4, 2004
31
hi kallen,

this is not too much difficult just to apply the Boolean Algebraic functions.I am also doing these things in these days as I have the course (Digital Logic design). I will give u the answer tommorrow.....for now m going to take a sleep zzzzzzzzzz
shall write ya,
susi

#### beautifulmind

Joined Mar 5, 2007
4
Look at the colors before the equal sign and after it, and see how it is applied in the example.
if you can visualise this i dont think you'll have a problem understadning and solving the rest. Match the colors and ull unederstand alot.

X'Y+X =X+Y
X+X' =1
Y+1 =1

A'B + A'BC + BC'D' +C'D
=B(A+A'C) + C'(BD'+D)
=B (A+C) + C'(B +D)
=AB +BC +BC' +C'D
=AB+B(C+C') + C'D
=AB+B(1) +C'D
=B(A+1) + C'D
=b(1) +C'D
=B +C'D

if this is understood let me know so i can continue solving the rest they are quite simple an straight forward if u want me to explain in details also let me know. All the best sile