During WWII (and indeed, during WWI), targeting calculations were carried out using electromechanical analogue computers. These used cams, gears, and linkages to solve the ballistic equations given estimates of the target's speed, course and range. For the heavy AA battery, these were obtained by the gunnery director tower, and then passed to the computer (in contemporary RN parlance, this was called a Table). The computer calculated the elevation and bearing for the guns, as well as the fuse settings. These were then passed to the gun crews using pointers and the fuse-setting machine by or in each turret. For the light AA battery, the offset directors had little automation - at first, these were little more than offset aiming positions, to prevent the vibration and smoke produced by rapid fire from interfering with aiming. Later models did, however, include some small analogue computers which allowed calculation of the lead-off distance for the guns. For more detail, you can see this comment, where I discuss the RN's anti-aircraft fire control procedures for light, medium and heavy AA guns.