The Half eggs would actually be the Type 909 Sea Dart directors, if I am looking at the same thing.
I don't think ADAWS would really be visible on a shipbucket drawing, as it is an combat management system. It would be visible in the ships design though; in the size of the CIC, computer rooms and the cooling of these spaces.
from the wikipedia article on the Type 82:
The advanced ADAWS-2 (Action Data Automation Weapons System Mk.2), a computer system designed to coordinate the ship's weapons and sensors.
The latter feature, although not externally apparent, was perhaps the most pioneering of the design; a leap forward from the rudimentary action information system of the "Counties" and its heavy reliance on manual data input.
...
The main advance in the design was with how the sensor data was processed and displayed. The ADAWS-2 system, based on two Ferranti FM1600 computers, integrated the identification, tracking and engagement of targets into a single system. ADAWS-2 could accept input from any of the ship’s radars or sonars, identify targets and produce continuous track histories. Using this information it could evaluate threat levels and control the engagement of targets using the relevant weapons systems. The whole process occurred almost automatically, requiring only oversight and command from the human operator. This new generation of warship would be commanded from an operations room within the ship rather than the traditional location of the bridge.
that is about the ADAWS-2 system though, the original ADAWS seems to have been trialled on board the Norfolk in 1970.