I have been trying to solve this problem but I am unsure whether or not this is the right procedure. I have the following truth table.
I need to find the expression for F as a product of sums and as a sum of products. I also need to find the minimal sum of products.
If I find the product of sums, do I have to convert it directly to sum of products? Or will the sum of products directly from the truth table be equivalent?
So far (lowercase c denoting complement):
My product of sums: F = (X+Y+Z) (Xc+Y+Z) (Xc+Y+Zc)
My sum of products: F = (XcYcZ) + (XcYZc) + (XcYZ) + (XYZc) + (XYZ)
Now for my attempt at the simplification to get the minimal sum of products
F = (X+Y+Z) (Xc+Y+Z) (Xc+Y+Zc)
= (0 + XY + XZ + YXc + Y + YZ + ZXc + ZY + Z) (Xc+Y+Zc)
= (Y (X+Xc) + Z (X+Xc) + Y + YZ + Z) (Xc+Y+Zc)
= (Y + Z + YZ) (Xc+Y+Zc)
= (Y+Z) (Xc+Y+Zc)
= YXc + Y + YZc +ZXc +ZY + 0
= Y (ZC+Z) + YXc + Y + ZXc
= YXc + Y + ZXc
= Y + ZXc
Any advice/tips and help would be greatly appreciated. Thanks!