Taking information as material to realize non-electronic physical computing is a promising idea, which facilitates the integration of technologies in different fields such as chemistry, biology, and mechanical control into a new computing platform. Here, we propose a novel, efficient and robust manipulation platform that drives droplet computing by way of inertial force. Combining this with droplet flow path design, we demonstrated multiple basic functions of droplet manipulation, including storage, dosing, interrupts, controllable release and addressing. These basic functions without external control lay the foundation for the realization of droplet calculation. We developed AND, OR, and XOR logic gates of the "liquid circuit" and combined them into a binary adder, which successfully completed the addition of four-digit binary numbers through droplet movement. Moreover, we attempted to perform algorithmic design for biological information under the control of droplets based on synchronous logical operations, developing the possibility of biological applications. This programmable physical computing system exists independently of electronic computing, aiming to supplement and expand the computing methods outside the field of electronic technology and to open a new method for the algorithmic operation of materials after combining new physical computing technologies such as biological or chemical computing.