Ship gun fire-control system
It could also automatically track the target by controlling the director's bearing power drive. Because of radar, Fire Control systems are able to track and fire at targets at a greater range and with increased accuracy during the day, night, or inclement weather. This was demonstrated in November 1942 when the battleship USS Washington engaged the Imperial Japanese Navy battlecruiser Kirishima at a range of 18,500 yards (16,900 m) at night. The engagement left Kirishima in flames, and she was ultimately scuttled by her crew. This gave the United States Navy a major advantage in World War II, as the Japanese did not develop radar or automated fire control to the level of the US Navy and were at a significant disadvantage.
The parallax correctors are needed because the turrets are located hundreds of feet from the director. There is one for each turret, and each has the turret and director distance manually set in. They automatically received relative target bearing (bearing from own ship's bow), and target range. They corrected the bearing order for each turret so that all rounds fired in a salvo converged on the same point.

The fire control switchboard configured the battery. With it, the Gunnery Officer could mix and match the three turrets to the two GFCSs. He could have the turrets all controlled by the forward system, all controlled by the aft system, or split the battery to shoot at two targets.
The assistant Gunnery Officers and Fire Control Technicians operated the equipment, talked to the turrets and ship's command by sound-powered telephone, and watched the Rangekeeper's dials and system status indicators for problems. If a problem arose, they could correct the problem, or reconfigure the system to mitigate its effect.

Mark 51 Fire Control System: The Bofors 40 mm anti-aircraft guns were arguably the best light anti-aircraft weapon of World War II., employed on almost every major warship in the U.S. and UK fleet during World War II from about 1943 to 1945. They were most effective on ships as large as destroyer escorts or larger when coupled with electric-hydraulic drives for greater speed and the Mark 51 Director (pictured) for improved accuracy, the Bofors 40 mm gun became a fearsome adversary, accounting for roughly half of all Japanese aircraft shot down between 1 October 1944 and 1 February 1945.

Mark 56 GFCS: This GFCS was an intermediate-range, anti-aircraft gun fire-control system. It was designed for use against high-speed subsonic aircraft. It could also be used against surface targets. It was a dual ballistic system. This means that it was capable of simultaneously producing gun orders for two different gun types (e.g.: 5"/38cal and 3"/50cal) against the same target. Its Mark 35 Radar was capable of automatic tracking in bearing, elevation, and range that was as accurate as any optical tracking. The whole system could be controlled from the below decks Plotting Room with or without the director being manned. This allowed for rapid target acquisition when a target was first detected and designated by the ship's air-search radar, and not yet visible from on deck. Its target solution time was less than 2 seconds after Mark 35 radar "Lock on". It was designed toward the end of World War II, apparently in response to Japanese kamikaze aircraft attacks. It was conceived by Ivan Getting, mentioned near the end of his Oral history, and its linkage computer was designed by Antonín Svoboda. Its gun director was not shaped like a box, and it had no optical rangefinder. The system was manned by crew of four. On the left side of the director, was the Cockpit where the Control Officer stood behind the sitting Director Operator (Also called Director Pointer). Below decks in Plot, was the Mark 4 Radar Console where the Radar Operator and Radar Tracker sat. The director's movement in bearing was unlimited because it had slip-rings in its pedestal. (The Mark 37 gun director had a cable connection to the hull, and occasionally had to be "unwound".) Fig. 26E8 on this Web page shows the director in considerable detail.
The explanatory drawings of the system show how it works, but are wildly different in physical appearance from the actual internal mechanisms, perhaps intentionally so. However, it omits any significant description of the mechanism of the linkage computer. That chapter is an excellent detailed reference that explains much of the system's design, which is quite ingenious and forward-thinking in several respects.
In the 1968 upgrade to USS New Jersey for service off Vietnam, three Mark 56 Gun Fire Control Systems were installed. Two on either side just forward of the aft stack, and one between the aft mast and the aft Mark 38 Director tower. This increased New Jersey's anti-aircraft capability, because the Mark 56 system could track and shoot at faster planes.

Mark 63 GFCS: The Mark 63 was introduced in 1953 for the twin QF 4-inch naval gun Mk XVI and Mk.33 twin 3"/50 cal guns. The GFCS consists of an AN/SPG-34 radar tracker and a Mark 29 gun sight.

Mark 68 GFCS: Introduced in the early 1950s, the Mark 68 was an upgrade from the Mark 37 effective against air and surface targets. It combined a manned topside director, a conical scan acquisition and tracking radar, an analog computer to compute ballistics solutions, and a gyro stabilization unit.
The gun director was mounted in a large yoke, and the whole director was stabilized in crosslevel (the yoke's pivot axis). That axis was in a vertical plane that included the line of sight.
At least in 1958, the computer was the Mark 47, an hybrid electronic/electromechanical system. Somewhat akin to the Mark 1A, it had electrical high-precision resolvers instead of the mechanical one of earlier machines, and multiplied with precision linear potentiometers. However, it still had disc/roller integrators as well as shafting to interconnect the mechanical elements. Whereas access to much of the Mark 1A required time-consuming and careful disassembly (think days in some instances, and possibly a week to gain access to deeply buried mechanisms), the Mark 47 was built on thick support plates mounted behind the front panels on slides that permitted its six major sections to be pulled out of its housing for easy access to any of its parts. (The sections, when pulled out, moved fore and aft; they were heavy, not counterbalanced. Typically, a ship rolls through a much larger angle than it pitches.) The Mark 47 probably had 3-D cams for ballistics, but information on it appears very difficult to obtain.
Mechanical connections between major sections were via shafts in the extreme rear, with couplings permitting disconnection without any attention, and probably relief springs to aid re-engagement. One might think that rotating an output shaft by hand in a pulled-out section would misalign the computer, but the type of data transmission of all such shafts did not represent magnitude; only the incremental rotation of such shafts conveyed data, and it was summed by differentials at the receiving end. One such kind of quantity is the output from the roller of a mechanical integrator; the position of the roller at any given time is immaterial; it is only the incrementing and decrementing that counts.
Whereas the Mark 1/1A computations for the stabilizing component of gun orders had to be approximations, they were theoretically exact in the Mark 47 computer, computed by an electrical resolver chain.
The design of the computer was based on a re-thinking of the fire control problem; it was regarded quite differently.
Production of this system lasted for over 25 years. A digital upgrade was available from 1975 to 1985, and it was in service into the 2000s. The digital upgrade was evolved for use in the Arleigh Burke-class destroyers.

The AN/SPG-53 was a United States Navy gun fire-control radar used in conjunction with the Mark 68 gun fire-control system. It was used with the 5"/54 caliber Mark 42 gun system aboard Belknap-class cruisers, Mitscher-class destroyers, Forrest Sherman-class destroyers, Farragut-class destroyers, Charles F. Adams-class destroyers, Knox-class frigates as well as others.

US Navy computerized fire control systems: 

Mark 86 GFCS: The US Navy desired a digital computerized gun fire-control system in 1961 for more accurate shore bombardment. Lockheed Electronics produced a prototype with AN/SPQ-9 radar fire control in 1965. An air defense requirement delayed production with the AN/SPG-60 until 1971. The Mark 86 did not enter service until when the nuclear-powered missile cruiser was commissioned in February 1974, and subsequently installed on US cruisers and amphibious assault ships. The last US ship to receive the system, USS Port Royal was commissioned in July 1994.
The Mark 86 on Aegis-class ships controls the ship's 5"/54 caliber Mark 45 gun mounts, and can engage up to two targets at a time. It also uses a Remote Optical Sighting system which uses a TV camera with a telephoto zoom lens mounted on the mast and each of the illuminating radars.

Mark 34 Gun Weapon System (GWS): The Mark 34 Gun Weapon System comes in various versions.