One by one, the umbilical cords of the electronic age are being cut.

First came walkie-talkies, then beepers, then cellular phones. Now come wireless computers, the latest gear designed to eliminate the notion that those doing the communicating can't move around at will.

Motorola Inc. yesterday joined a handful of other companies in announcing its plans to explore ways for computers to send and receive data over radio waves, without requiring physical hookups to cables or phone lines.

The company's "wireless in-building network" technology is designed to enable computer users within a building to move from place to place without having to string new wire or sit near a cable connection to stay linked to other terminals on the office's central data communications network.

The idea is similar to a scheme Apple Computer Inc. sketched out in a filing with the Federal Communications Commission earlier this month that would allow portable-computer users to form ad hoc groups and communicate over radio waves instead of cable.

Under Apple's plan, a college student relaxing in a lounge might access the computerized card catalogue of the school's library. Or people attending a sales staff meeting in a hotel ballroom might zip their financial projections through the air to one another's computers.

The ideas outlined by Motorola and Apple, as well as a similar product announced by NCR Corp., are just the latest additions to the wireless world now taking shape. "The bigger picture is to provide as much communications capability as possible to anyone, anywhere, anytime... . The whole point is communications will be where the person is rather than the person going to where the communications is," said Henry Goldberg, a Washington telecommunications attorney who represents Apple and other companies.

Thus the images once confined to science fiction draw closer to reality: Chatting on a pocket phone as you walk down a busy street, sending in a lengthy report while sunning on the beach, receiving a fresh map while driving to an appointment.

The system described by Motorola yesterday would handle just the last few feet of data communications within a building. The company has in mind turning a building into a cluster of invisible "micro-cells," a small-scale version of the way cellular phone providers divide up the landscape into geographic units.

Computers would be equipped with high-frequency transmitters and receivers so that users could freely move them around a building, forgoing the $200 to $3,000 Motorola says it can cost to rewire a desk for a computer. The company plans to offer products using the technology next year.

Motorola has already made it over one major hurdle -- that of winning from the FCC the rights to use certain frequencies in the increasingly crowded spectrum of airwaves. By grabbing frequencies not normally used for commercial services, Motorola said it has been able to secure the rights to such in-building wireless networks in roughly 300 areas of the country.

Motorola's stock rose 12 1/2 cents yesterday in response to the announcement.

Introduction of the networks is the latest of several moves by Motorola to shore up its position in wireless communications. The company's most ambitious undertaking is Iridium, a proposed network of 77 satellites that would allow people to make and receive phone calls from remote locations anywhere in the world.

After watching its dominant share of the "wireless" area being nibbled away by competitors over the last decade, Motorola has finally made "a vigorous attempt to make sure it is at least doing something in every wireless market," said Ken Bosomworth, president of International Resource Development Inc., a New Canaan, Conn., consulting firm.

Apple's interest in the wireless market has more to do with its struggle to find an acceptable way to connect computers in large companies. A wireless capability could allow Apple to reassert itself in the corporate PC network market, he said, but added, "I don't think they stand a prayer."