The way Michael Johnson figured it, when he graduates from Ballou High School next spring, he will be ready for college. But the question he had for college recruiters who came to his Southeast Washington neighborhood yesterday was whether any college would have a scholarship for him.

"I rate myself as a very upstanding gentleman," said Johnson, 17, during an interview with a recruiter for Morehouse College in Atlanta. "I take care of myself, I'm strong-minded and I have courage. My problem is that I don't have enough money."

The recruiter, Henry Thompson, who doubles as a computer science instructor at Ballou High, nodded with understanding and turned to a computer terminal -- the Guidance Information System -- that listed most of the four-year colleges in the United States, admission requirements and information on $450 million worth of scholarships.

Johnson, who said he sells shoes part time to make money for college, became excited. "I want to be a professional in marketing," he said. "Can this help me be a success?"

His interest was a slice of the seventh annual Operation College Bound, an event sponsored by the Fort Davis branch of the D.C. Public Library, where students and parents living in the sometimes forgotten neighborhoods of Southeast Washington can meet with representatives of some of the finest colleges in the nation.

Against a backdrop of cutbacks in federal aid for education and record unemployment, about 50 students showed up, most them unfailingly optimistic that somehow they would realize their dream of going to college.

On hand to encourage them were representatives from about 20 schools, ranging from Amherst College in Massachusetts to the Maharishi International University of Natural Law in Iowa.

Johnson, in his search for money to attend college, was given a list of places to write for more information. "I'm just trying to do the best I can every day, learn all I can every day," he said. "That's my key to success, whether I have the money or whether I don't."

According to the United Negro College Fund, the average black college student comes from a family earning roughly $11,000 a year -- half the average earnings of families of white college students.

Nearly 76 percent of black college students in 1980 came from families whose parents never attended college, according to a survey by the National Urban League. And because of changes in the eligibility requirements for Social Security Educational Benefits in 1981, which curtailed the amount of federal assistance available, many college students from low-income families will no longer be able to attend, the survey said.

"Reagan has severely hurt the average college student," said Henry Thompson, the Morehouse recruiter. "We had 10 students from Washington who could not return to college this year simply because they didn't have the money. This summer was the worst I've seen. We had 30 students looking for summer jobs so they could stay at Morehouse, and we only found work for half of them. The truth is, the situation about going to college is sad."

Cynthia Bridgett, a 16-year-old Ballou High computer whiz, said she believes her academic skills will get her the scholarship that will enable her to attend college.

"I could graduate next spring, or I could wait and finish my senior year like everybody else," she said. "I just don't know what to do. I could use some financial aid, but I know I'm going to some college."

"You hear a lot of bad things about the D.C. school system, but I didn't see any evidence of it today," said Karen Bates-Logan, a recruiter for Wellesley College. "These were some very confident kids. They don't feel that because they went to Ballou instead of Georgetown Prep that their chances have been lessened. They actually feel that they will be an asset to the school that gets them."