To determine the angle of the shaft being measured based on the output value of an $8-$bit absolute rotary encoder, we need to know the specific encoding scheme used by the encoder. The output value you provided, $00100110,$ represents the binary representation of the encoder's output.However, without knowledge of the encoding scheme, it is not possible to directly convert the binary value to an angle. The encoding scheme determines the mapping between the binary code and the corresponding angular position.Different encoding schemes can be used, such as binary, Gray code, or other custom mappings. Each scheme has its own unique mapping of binary codes to angles.If you have information about the specific encoding scheme used by the encoder, I can help you convert the binary value to the corresponding angle.