Sensing capabilities as an integral part of the network have been identified as a novel feature of sixth-generation (6G) wireless networks. As a key driver, millimeterwave (mmWave) communication largely boosts speed, capacities, and connectivity. In order to maximize the potential of mmWave communication, precise and fast beam acquisition (BA) is crucial, since it compensates for a high pathloss and provides a large beamforming gain. Practically, the angle-of-departure (AoD) remains almost constant over numerous consecutive time slots, the backscatter signal experiences some delay, and the hardware is restricted under the peak power constraint. This work captures these main features by a simple binary beam-pointing (BBP) channel model with in-block memory (iBM) [1], peak cost constraint, and one unit-delayed feedback. In particular, we focus on the sensing capabilities of such a model and characterize the performance of the BA process in terms of the Hamming distortion of the estimated channel state. We encode the position of the AoD and derive the minimum distortion of the BBP channel under the peak cost constraint with no communication constraint. Our previous work [2] proposed a joint communication and sensing (JCAS) algorithm, which achieves the capacity of the same channel model. Herein, we show that by employing this JCAS transmission strategy, optimal data communication and channel estimation can be accomplished simultaneously. This yields the complete characterization of the capacity-distortion tradeoff for this model.