Frances Elizabeth Holberton, one of the first computer programmers, whose contributions to software over the years ranged from an early data-sorting program to helping develop the business programming language Cobol, died on Dec. 8 at a nursing home in Rockville, Md. She was 84.

The cause was heart disease, diabetes and complications from a stroke that she suffered several years ago, according to her daughter, Priscilla Holberton of Silver Spring, Md.

''Betty Holberton was a real software pioneer,'' said Donald E. Knuth, a professor emeritus at Stanford University and author of the three-volume ''The Art of Computer Programming,'' the profession's defining treatise.

Mrs. Holberton, a graduate of the University of Pennsylvania, was one of the six young women recruited by the Army to program the Electronic Numerical Integrator and Computer, which became known by its evocative acronym, Eniac. The Eniac is credited with being the first all-electronic digital computer.

The Eniac's job was to calculate the firing trajectories for artillery shells. The young women programmers were selected for their skills in mathematics. The work they did was ''hard-wired'' programming, laboriously setting switches and cables inside the 30-ton black behemoth of a machine.

Mrs. Holberton, colleagues recall, was particularly adept at figuring out the best path for guiding the complex calculations through the electronic labyrinth of the Eniac. Frequently, these insights came to her overnight.

''Betty had an amazing logical mind, and she solved more problems in her sleep than other people did awake,'' recalled Jean J. Bartik, another of the Eniac programmers.

The Eniac was demonstrated in February 1946, too late for use in World War II, but it helped open the door to modern computing. The Eniac programming team broke up, but Mrs. Holberton was the one of the six who stayed longest in the field.

After the war, she joined the Eniac designers, John Presper Eckert and John W. Mauchly, in their effort to develop the Univac, an early commercial computer, which was introduced in 1951. While working on the Univac, Mrs. Holberton did some of her most innovative work. She developed a program for sorting and merging large data files, which at the time were stored on reels of magnetic tape. Any such updating of data files was an arduous programming task at the time, and her program vastly simplified that job.

''That was a huge tour de force,'' said Paul E. Ceruzzi, a computer historian at the Smithsonian Institution.

In 1953, Mrs. Holberton joined the Navy's Applied Math Lab at the David Taylor Model Basin in Maryland as the supervisor of advanced programming, where she worked until 1966. In 1959, she was a crucial member of the committee that developed Cobol, or Common Business Oriented Language. The committee worked for six months on the standards and specifications for a business programming language, which was introduced in 1960.

The committee's work was seen as a temporary solution to the growing problem created by the increasing need for a standard programming language for handling business data at a time when computing was moving into the mainstream of the corporate world. Yet Cobol, updated many times over the years, is still widely used.

Computer scientists often criticize Cobol as a hasty, inelegantly designed programming language. But it gave computing a way to handle and visually describe business data, making it easier to program business problems on computers.

Mrs. Holberton, who joined the National Bureau of Standards in 1966 and worked there for two decades, once echoed those views. In a 1983 interview conducted for the Charles Babbage Institute, a computing history center at the University of Minnesota, Mrs. Holberton conceded some of the criticisms of the language she helped develop. But, she added, ''Cobol, I felt, was very important because of its ability to describe data.''

According to Kathryn Kleiman, a lawyer who is working on a documentary film on the women in the Eniac program and their contribution to the field, Mrs. Holberton consistently worked on trying to make computers easier to program.

''She took that hard-won knowledge on the Eniac and applied it over the next 40 years, in nearly everything she did in the field,'' Ms. Kleiman said.

In addition the her daughter Priscilla, Mrs. Holberton is survived by her husband, John Vaughn Holberton, and another daughter, Pamela Holberton, both of Rockville.

Photo: Frances E. Holberton, in 1997.