The use of a simple hybrid cellular automaton (combining rules 90 and 150 in Wolfram's notation) as a built-in self test (BIST) structure for VLSI systems is considered. Two six-bit pseudorandom number generators based on cellular automata (CA) and LFSR have been designed using 2μm design rules for an N-well CMOS process. Layout has been achieved using ChipWise. Comparative performance studies of these CA-based new pseudorandom number generators and the LFSR-based generators show the great advantage of these CA-based BIST structures over the LFSR. The group and semigroup algebraic properties of 1-D null bounded elementary cellular automata with the linear evolution rules 90 and 150 are also presented and discussed, together with their state transition graphs. The variety of symmetries of these CA systems results in a multiplicity of functional dependences for the group and semigroup orders of the associated algebraic structures and the CA length N.