This article is about the position control of a binary hyper redundant manipulator, which is driven by pneumatic on-off actuators. The end platform of the binary hyper redundant manipulator bears a small fine tuning manipulator, which is a continuously actuated six-joint manipulator attached as a versatile error-compensation tool. It is employed to compensate especially the discretization errors. The position control aims to make the end-effector of the fine tuning manipulator track a specified sequence of successive poses as required by the task to be performed. This aim is achieved by solving the inverse kinematics problem of the binary hyper redundant manipulator, i.e. by determining the binary positions of the on-off actuators, so that the end platform of the binary hyper redundant manipulator enters the inverted working volume of the fine tuning manipulator for each specified target pose of the end effector. As to solve the inverse kinematics problem of the binary hyper redundant manipulator, three methods are presented. They are the plain spline fitting method, the extended spline fitting method, and the workspace filling method. The plain spline fitting method is based on forcing the actual backbone curve of the binary hyper redundant manipulator to approximate a spatial reference spline which is specified as the desired backbone curve. In the extended spline fitting method, the result found in the plain spline fitting method is improved by using a genetic algorithm. In the workspace filling method, the workspace of the binary hyper redundant manipulator is filled randomly with a sufficiently large finite number of discrete configurational samples. If it is desired to have a concentration on a particular region of the workspace, then that region is filled by using a genetic algorithm. After the filling stage, the sample closest to the desired configuration is determined by a suitable searching algorithm. The three methods are demonstrated and comparatively discussed by means of several examples.