Apparatus and methods for power amplifiers are disclosed. The system includes an insertion module for holding a proximal end of the steerable array and a force sensor configured to detect force on the steerable array and to produce force information. In one embodiment, the bracket includes one or more locking tabs on the rotary cover aligned in coplanar relation to the rotary cover and cooperatively mating with cutout portions in the base. This arrangement enables dynamic adjustment of the counter electrode voltage of the liquid crystal panel in response to a dynamic change in amount of the illumination light for irradiating the liquid crystal panel. The logic system includes a first clock domain, which performs logic operations and scan tests with a first clock signal, and a second clock domain, which performs logic operations with a second clock signal and performs scan tests with the first clock signal. Computation of the sum proceeds substantially simultaneously with and without the rounding input, and rounding logic makes a selection later in the computation.