NEW YORK (FORTUNE Magazine) - Can Cisco Systems, a technology giant best known for making the routers and switches that drive traffic around the Internet, capture the hearts, minds and remote controls of television viewers?

That's the multi-billion dollar question now facing the Silicon Valley firm. In one of the largest acquisitions in its 22-year history, Cisco (Research) spent $6.8 billion about six weeks ago to buy Scientific Atlanta (Research), a company that makes cable TV set-top boxes.

For the deal to pay off, Cisco needs to anticipate how viewers want to watch TV, and then sell its vision to cable TV operators, to big phone companies like Verizon (Research) and AT&T (Research) that are getting into the TV business and, ultimately, to viewers.

"Our goal," says Cisco CEO John Chambers, "is to be the key player in the home."

With that in mind, Chambers led a delegation of top Cisco brass to Atlanta, where the cable industry held its big (about 16,000 people) annual convention this week. Their sales pitch went something like this: TV is becoming more like the Internet - available on demand, on portable devices, with a vast menu of choices and with the consumer in control - and no one knows the Internet better than Cisco.

"This is a market transition that's already occurring," said Chambers. "You can't stop it."

"I love basketball," he explained. "I want my basketball games to follow me anywhere. On any device."

Chambers, who is known as a great salesman, has a knack for simplifying technology. On a CEO panel at the cable convention, he talked about basketball, about empowering consumers and about a vision he called "The Connected Life." By contrast, Ed Zander, the CEO of Motorola (Research), which is Cisco's biggest competitor in the set-top box arena, talked about "seamless mobility," which is not an easy idea to get your head around.

Behind the buzzwords are some intriguing possibilities. Mike Volpi, the senior vice president of Cisco's routing technology group, who is overseeing the integration of SA, told me that Cisco would like to enable viewers to sit in front of their TV sets and easily get video from any source they want - their video provider (whether cable or a telco), the Internet, where sites like www.youtube,com and Google (Research) video make programming available, or their own computers, where home movies and photos are stored.

And with companies like The Walt Disney (Research) Co. and Time Warner (Research) (FORTUNE's parent) putting more TV shows on the Internet, the idea of easily connecting the PC to the TV is a timely one.

It's not just that TV is becoming more Internet-like. Young viewers in particular want to be control. "The thing people like about the Web is that it's very personalized," Volpe says. "It orients itself around you, the user. And it's highly interactive."

Bob McIntyre, the chief technical officer of Scientific Atlanta, fleshed out the vision a little more. He demonstrated a new set-top box that includes a digital video recorder with 80 hours of storage, a DVD player and a DVD burner. With that, a viewer could order a movie from a cable operator and burn it onto a DVD. This saves the consumer a trip to Blockbuster (to rent a movie) or to Wal-Mart (Research) (to buy a DVD), and makes the cable operators the new middlemen in selling DVDs. For a firm like Time Warner, which owns a movie studio, HBO and cable systems - and just happens to be SA's biggest customer - this could be appealing.

Here's another peek into the future, according to Cisco. Big cable operators want to sell customers a so-called "quadruple play" - TV, phone, Internet access and cell phone service, though a partnership with Sprint Nextel (Research). All the services would be networked. That would give viewers caller ID. It would enable them to program their digital video recorders from their cell phones. And - get this - it would allow you to sit at home and, by combining GPS technology and Internet maps, track the locations of all the cell phone users in your family at any given time. Teenagers will love the idea that parents can monitor their every move - not.

None of this technology is especially complicated, but none of it is easy to use, either. That brings us back to the question of whether a business-to-business technology provider like Cisco can become consumer-savvy and consumer-friendly.

"It's a fair question," Volpi says. As it happens, Cisco has been selling home networking products directly to consumers and small businesses since 2003 when it acquired Linksys. Since then, Linksys has doubled its sales from about $500 million to $1 billion. "We dipped our toe in the water with Linksys," he says, "and the experiment has worked pretty well."

Home networking, of course, appeals mostly to people who are comfortable with technology, since it is about sharing broadband connections and connecting computers to each other and to peripheral devices. By comparison, watching television has been blissfully simple.

Then again, as cable operators compete with the satellite companies and, soon, with the telcos, they have begun to sell a broader range of products and services - not just TV networks, but DVRs, video on demand, and voice over Internet protocol.

Cisco must feel right at home.