Virgil T. Murphy leaned in and studied the computer screen. The problem: "2+-6=?"

Murphy thought for a second. Then he punched up "-4." In less than a flash, the screen read: "GOOD, VIRGIL T. MURPHY. THAT'S RIGHT. TRY ANOTHER ONE."

During the decade that ends next week, computerized arthimetic drills like this one became enormously popular in the nation's high schools. But for senior Virgil T. Murphy and his fellow students at Ballou High School, the 1980s are about to bring a computer that will affect virtually every aspect of school life.

In March, Ballou, at Fourth and Trenton streets SE, is expected to take delivery of a new $500,000 computer system.

The new system will replace Ballou's current $100,000 model. It will train an average of 2,000 students a week in programming, and will serve as an important teaching tool for math and science classes.

But "the exciting part" said Henry Thompson, Ballou's 35-year-old director of data processing, is that within five years, the computer will move into the actual administration of the school -- with students handling much of the programming and keypunching.

Among other chores, the computer will collect attendance, keep track of the school's electricity and heating use patterns, schedule teacher vacations, even order string beans for the cafeteria.

The new computer is the most dramatic proof yet that Ballou's four years as the city's designated math and science high school have brought results. The arrival of the new computer has been roundly hailed by school system officials, Ballou officials -- and students themselves.

"We get 1,500 students a year coming out of here and going straight into the job market," said Dennis C. Johnson Jr., Ballou principal. "This is what they need to have. So this is the way we have to keep on going."

"This is the kind of training I'm going to need to become a computer technician when I grow up," said Cynthia Jackson, a 14-year-old freshman who lives at 1447 Savannah St. SE. "I think it's great."

"We need, throughout the system, to have computer facilitation of much of the management mess," said James Guines, associate superintendent for instructional program development and services. The system at Ballou "is going to play a major role," Guines said.

The most visible immediate day-to-day benefit of the new system, according to Thompson, will be that about 2,000 students a week will be able to train on a computer. About 750 students a week use the present system. Because Ballou offers specialized math and science courses, about 120 of the 750 computer-users are bused to Ballou from all over the city.

In the four and a half years Ballou has operated under its "old" computer system, about 50 students a year got computer-related jobs right after graduation. Thompson said he expects that average to "maybe double" under the new system.

"It wouldn't surprise me" Thompson said. "We've got kids here who can write a program that will tell you what the babies will look like 20 generations from now if you mate white rats and black rats.

"Because we're the math and science school, these kids have much more motivation than usual. I know it's very difficult to convince the world that high school kids can do programming and do it well, but I know these kids can."

So does the D.C. Fire Department. Last year, under Thompson's direction, Ballou students conducted an analysis of every fire in the city the previous year.

After sorting out fire reports according to type of dwelling, time of day and amount of damage, the students wrote a computer program to assess the data. The computer then spewed out a plan to help fire officials tailor their training to the most frequent kinds of fires.

"They were absolutely flipped by the work the kids did," Thompson said.

Such success has increased interest in Ballou's computer courses, and according to S'Antonio Goode, of 82 Elmira St. SW, a 17-year-old senior who has worked with Thompson for three years, overcrowding is a major problem. w

"There's a lot of people in here, and sometimes you've got to wait to get on a terminal," Goode said. "Nobody likes to wait."

"But I guess I'm not too surprised. You can make $40,000 a year as a computer traffic manager."

The new Ballou system's memory capacity will be 370 million characters, compared with 21 million in the old system. The system will "understand" six computer "languages" (up from three), and will be fitted with telephone links to terminals in every one of the city's 105 schools (up from 14).

In 1977, under the old computer, Ballou's training program was rated "exemplary" by a national panel of teachers. The school was one of only 109 in the country to attain that rating, and one of only three in the Washington area.

What will the new system bring? "Well," said Thompson, "as you can see, it's a vacant period, and this room is full."