We have developed a bio-inspired electronic computing system, the 'electronic amoeba'. This system was designed to search for a solution to a combinational optimization problem, as inspired by foraging behavior of a single-celled amoeboid organism that is trying to maximize its food intake while satisfying given constraints. We electronically implement the system and demonstrate its solution search capability for solving the Boolean satisfiability problem, SAT. We apply the electronic amoeba to autonomous walking control of a multi-legged robot. Each leg joint has three-valued state and the electronic amoeba successively searches for a combination of the leg joint states to satisfy the objective of moving straight depending on the state of the robot.