Forget the sophisticated new gadgets and gizmos attached to that multiline, six-button telephone: in the federal government it's the single-line phone that's on its way in.

In the past three years, the General Services Administration has torn out 31,100 multibutton keysets and installed 27,100 single-line telephones in the Washington region alone.

"We consider this to be a more cost-effective means of providing the same service to federal workers; exactly the same service and in some ways better," said Donald L. Hardesty, the GSA's director of telecommunications, said.

With the introduction of state-of-the-art electronic wizardy, these single-line telephones are easier to install, cheaper to move and do the same job for $46 a year less: $146 compared to $192.

That means, Hardesty said, that over the next five years federal workers will be asked to give up their hold buttons and speed-dialing cards for three-digit codes that will provide those services and more, such as intercom service, conference call connections and call-forwarding to a designated number.

Cost-saving efforts by President Carter began the drive toward reducing government telephone costs, Hardesty said, but it wasn't until President Reagan took office--and named Gerald P. Carmen as GSA administrator--that things began to move quickly.

GSA officials estimate that $14 million a year in telephone costs can be saved by switching to the single-line system, by using competitive bidding to install the systems and by "tiering" the service to federal employes--giving a worker only the access the individual needs.

Hardesty said the savings increase when the costs of moving telephones is included. In the Washington area alone, GSA spent $4.3 million in fiscal 1982 moving telephone lines from one place to another. It costs $75.18 to move a six-button set, but only $38.81 to move a single-line set.

The technology that made single-line phones the optimum instrument for the federal government grew from the development of sophisticated electronic equipment in the early 1970s. In the late 1970s, the federal government began to buy the systems in conjunction with new policies designed to consider soliciting bids from companies beyond the Bell System.

The new "tiering" concept involves five levels of service:

* The basic standard level service would give about 10 percent of the government's workforce sets that can call only another government telephone. Only those workers involved with other federal agencies in their jobs, such as clerks, would receive this service. These employes would not be allowed to call any commercial telephone numbers on their sets.

* The second tier would add access to the surrounding "local serivce" area. This service is expected to be given to one in four federal workers.

* The third tier allows employes to tie into the Federal Telecommunications System (FTS) long-distance lines but bars local calls. Again, only about 10 percent of the workforce would have that system.

* Most government employes--about half--would receive the fourth-tier service: full access to all government and commercial numbers.

* The most exclusive service, the fifth tier, would allow employes to make international calls.

"This change in philosophy can reduce local . . . charges, commercial toll charges and FTS intercity calling because managers can restrict an employee to only those services he needs to do the job," according to a GSA fact sheet.

The tiered service is mandatory, Hardesty said, whenever an agency changes its telephone configuration, expands or contracts its operation in any given location.