Why was battleship fire control so difficult to armour?

Why were fire-control systems, including those on Bismarck, so difficult to protect against battle damage?

Directors need a high, unobstructed view, which leaves them exposed above the main armour; designers can protect the transmitting paths and plotting spaces below, but not turn the upper director into a fully armoured citadel.

Primary and secondary fire-control positions sit high because they need long sight lines over the ship and horizon. That elevation places them outside the thick central armour and exposes them to shellfire and splinters. Designers can run protected tubes down to plotting rooms and place more of the calculation system below decks, preserving part of the chain after upper damage. Nelson's tall bridge structure also tried to move directors away from the line at which enemy guns were expected to aim. The superstructure itself could still be hit, so fire-control survivability depended on redundancy and protected connections rather than making every director invulnerable.