Last August, U.S. District Judge Barrington D. Parker was presiding over a case involving a discrimination complaint, a common but often tedious task for federal judges in Washington, when his courtroom clerk, Elizabeth Flynn, handed him a note.

"Judge, you've been assigned the Hinckley case," it said.

That morning, a federal grand jury had indicted John Warnock Hinckley Jr. on charges that he attempted to assassinate President Reagan. Parker, 66, his name pulled at random from a stack of shuffled cards, would preside over what will doubtless be one of the most widely publicized and historically significant cases to pass through the federal courthouse here.

When cases are heard by a jury, as the Hinckley trial will be when it begins Tuesday, the judge customarily acts as an umpire, resolving disputes between the prosecution and the defense about the evidence and how to present it.

Parker, however, has often taken a more aggressive role in the cases before him, frequently interrupting lawyers to question a witness himself. It is a habit that lawyers complain about privately and one that Parker says he knows he should try to restrain. Yet he admits he sees himself playing more than a passive role in the Hinckley case.

"I certainly don't perceive myself as just calling strikes and balls. No, I don't," Parker said during a recent interview in his chambers.

Strict decorum is the rule when Parker is on the bench, down to a deputy marshal's warning that no overcoats are to be draped over the seats while court is in session. Newspapers are to be kept out of sight, whispering is frowned upon, and both attorneys and defendants have felt his wrath.

Appointed to the federal bench by President Nixon in 1969, Parker has had his share of the spectacular--and the mundane--during the 12 years he has been a judge.

In 1979, he told President Carter that Carter could not punish violators of his wage-price guidelines, a ruling later reversed in the appeals court. Later that same year, Parker ordered the Army to upgrade to "honorable" discharges it had given to 10,000 Vietnam-era veterans who had been forced to undergo testing for drug abuse.

In other rulings, Parker ordered in 1975 that the D.C. government fill 100 staff vacancies at D.C. General Hospital, where Parker said the quality of care was "well below any acceptable level." In 1974, Parker told the Federal Aviation Administration that it could not use X-ray machines as security devices at the nation's airports until they assessed the impact on the environment and obtained comments from the public on the machines, which are used to examine carry-on luggage.

A graduate of Dunbar High School, Lincoln University and the University of Chicago Law School, Parker also holds a master's degree in economics from the University of Pennsylvania and worked as a government economist during World War II. He was the president of the D.C. Federation of Civic Associations and was an active Republican, attending national conventions and bucking the party in 1964 by refusing to support presidential hopeful Barry Goldwater.

In November 1975, Parker was struck by an automobile on Connecticut Avenue NW as he was heading to American University to teach a class. His left leg had to be amputated as a result of the injuries and he now walks with crutches.

On the bench, Parker has been known to be cantankerous, at times unsparing with his sharp remarks for attorneys and defendants who appear before him. During one pretrial hearing, Parker snapped at Hinckley that he was to stand when he addressed the court. Hinckley, who had been sitting back in his chair at the defense table, jumped to his feet.

Parker dished out some of his harshest words to former CIA director Richard M. Helms, who got a $2,000 fine and a two-year suspended jail sentence from Parker in 1977 for refusing to tell a congressional committee about CIA operations in Chile. Helms had pleaded "no contest" to the charge.

"You now stand before this court in disgrace and shame," Parker told Helms. "Public officials at every level, whatever their position, like any other person, must respect and honor the Constitution and the laws of the United States," he said.

Hinckley's chief defense lawyer, Vincent J. Fuller, was before Parker in another controversial case, involving a guilty plea by the Westinghouse Electric Corp. on foreign bribery charges.

Parker delayed acceptance of the 1978 plea-bargain agreement between the Justice Department and Westinghouse, in which the company said it would pay a $300,000 fine, until the identity of the foreign official involved in the case--an Egyptian deputy prime minister--was disclosed.

Parker appeared in the federal court in November 1980, not as a judge but as a witness, to deny, under questioning by the U.S. attorney, a police informant's allegation that Parker had been at the home of a defendant who came before him in a drug case. The judge who presided at the closed hearing said that it was obviously "a case of mistaken identity and I question somewhat the source," according to a transcript of the proceeding.

In 1979, heavy security measures, like those that will be used in the Hinckley case, surrounded another highly publicized trial in Parker's sixth-floor courtroom. It was the case of two anti-Castro Cubans accused of the car-bombing assassination of former Chilean ambassador Orlando Letelier. During that trial, Parker received a threatening letter, delivered to his home.

The two Cubans were convicted, but in 1980 the appeals court said Parker had improperly allowed some evidence to be introduced at the trial and reversed the case. Spared the life sentences that Parker had imposed on them, the two men were retried last summer, in Parker's courtroom again, and were acquitted.

Less than three months had passed after the second Letelier trial when Parker learned he would preside at Hinckley's trial.

"I said, 'Well, this is interesting," Parker recalled. But, he added, "except for the fact that the president is involved, this is a run-of-the-mill case."