Comp-u-Staff Inc., a national data processing firm headquartered in Towson, has promoted Kathleen K. Cornell to president and chief executive officer, and Douglas O. Sharp to vice president of the 6-year-old firm, Chairman Hank Post announced.

Cornell has been with the firm for five years, most recently as general manager of administration and finance, while Sharp, after four years with Comp-u-Staff, has served as general manager of applications support.

Compucare Inc., a McLean information processing firm servicing the health care industry, has appointed Gary Hammon vice president in charge of its PCI Systems division, which sells software to hospitals using IBM mainframe computers. Hammon, formerly vice president for business affairs at the University of Texas, San Antonio, succeeds Roy P. Fisher who has resigned.

Barbara Hackman Franklin has been elected to the board of directors of Automatic Data Processing Inc., a computing services firm based in Roseland, N.J.

Hackman, a former member of the U.S. Consumer Product Safety Commission, heads her own management consulting firm in Washington and is expected to be reappointed by President Reagan to the Advisory Committee for Trade Negotiations.

OPUS Corp., a software firm in Germantown, has appointed Dennis Chapman director of national sales and marketing. The firm also named new marketing specialists: Mark Jennings, Steve Balducci and Jeff Loftus.