Shannon development means the developing of a boolean function
after one variable
So does the Shannon developing after variable xi mean:
f(x1,..,xn) = xi AND f(x1,...,xi-1,1,xi+1,...xn) v xi! AND f(x1,...,xi-1,0,xi+1,...xn)
f(x1,x2,x3,x4) = x1x2 v x3x4
Development after x1:
x1(1 AND x2 v x3x4) v x1! (0 AND x2 v x3x4) =
x1(x2 v x3x4) v x1! (x3x4)
From this equation one can easier see that if x1=0, then x3 and x4 have to be 1, so that this combination of variables can make the function true(=1).
If you develop the equation after all variables the formula will be in the complete disjunctive normal form, which shows you all the variable combinations, which make the function true.
For this formula the cDNF looks like:
x1x2x3x4 v x1x2!x3!x4 v x1x2!x3x4 v x1x2x3!x4 v !x1!x2x3x4 v x1!x2x3x4 v !x1x2x3x4
Every variable can be replaced with a 1 and each negated variable can be replaced with a 0. These are the combinations for which the function is true.
Methods to get die cDNF are boolean cube and Quine-McClusky.