On May 25, 1941, Ms. Fawcett was among those in Hut 6 briefed on the search for the Bismarck.

“We all knew we’d got the fleet out in the Atlantic trying to locate her because she was the Germans’ most important, latest battleship and had better guns and so on than anybody else, and she’d already sunk the Hood,” Ms. Fawcett recalled in the book. “So it was vitally important to find where she was and try to get rid of her.”

She was just over an hour into her shift when she typed out a message from the main Luftwaffe Enigma. Reading the message, she recognized that a Luftwaffe general whose son was on the Bismarck had sought to find out if he was all right and had been informed that the ship, damaged in the previous battle, was on its way to France — to the port of Brest, in Brittany — for repair.

The message, passed instantly along the chain of command, was instrumental in finding the Bismarck, which was first spotted from the air by a seaplane and subsequently attacked by aircraft carrier torpedo bombers and swarmed by Royal Navy battleships and cruisers. It was sunk in the Atlantic west of Brest on May 27.

Janet Carolin Hughes was born on March 4, 1921 — probably in Cambridge, where her paternal grandmother lived, her son said, though her family lived in London. (There is some uncertainty about her middle name; Mr. Smith said that it was Caroline at birth and that Ms. Fawcett dropped the e later on, just as she dropped the t in Janet.) Her father, George Ravensworth Hughes, was a lawyer for the guild known as the Goldsmiths’ Company; her mother, the former Peggy Graham, did charitable work as a prison visitor.

As a girl, Jane aspired to be a ballet dancer and trained for a year at Sadler’s Wells, but at 17 she was deemed too tall for the company; as a consolation, her parents sent her to Switzerland, where she spent six months studying German. Her mother called her back for debutante season, insisting it was time for her to come out in society.

Resentful of this turn of events, she applied to work at Bletchley after receiving a letter from a school friend who was already there. It was the winter of 1940, and she was 18.