One-dimensional Cellular Automata (CA's) are considered as potential pseudorandom pattern generators to generate highly random parallel patterns with simple hardware configurations. A class of linear, binary, and of nearest neighbor (radius = 1) CA's is referred to here as elementary ones. This paper investigates operations of such CA's with fixed boundary conditions when non-null boundary values are applied to them. By modifying transition matrices of elementary CA's to include the influence of boundary values, structures of state transition diagrams are determined.