An optical four-bit parallel-shift register that consists of four serially connected optical flip-flop memories is driven by common clock pulses. Each optical flip-flop consists of two coupled polarization switches that share an all-optical demultiplexer, which makes the optical flip-flops easily connected with each other to form a parallel-shift register. The optical flip-flops are controlled by clock pulses. The parallel-shift register and an optical parallel adder are used to demonstrate an all-optical binary multiplier and its optical control circuit. The concept is demonstrated at an operation speed of 10 MHz for registers and 1 MHz for a multiplier, which is limited by long laser cavities formed by the optical fiber.