The study, by Common Sense Media, a San Francisco nonprofit group, is the first of its kind since apps became widespread, and the first to look at screen time from birth. It found that almost half the families with incomes above $75,000 had downloaded apps specifically for their young children, compared with one in eight of the families earning less than $30,000. More than a third of those low-income parents said they did not know what an “app” — short for application — was.

“The app gap is a big deal and a harbinger of the future,” said James Steyer, chief executive of Common Sense Media, which had 1,384 parents surveyed this spring for the study. “It’s the beginning of an important shift, as parents increasingly are handing their iPhones to their 1 ½-year-old kid as a shut-up toy. And parents who check their e-mail three times on the way to the bus stop are constantly modeling that behavior, so it’s only natural the kids want to use mobile devices too.”

The study found that fully half of children under 8 had access to a mobile device like a smartphone, a video iPod, or an iPad or other tablet. Of course, television is still the elephant in the children’s media room, accounting for the largest share of their screen time: about half of children under 2 watch TV or DVDs on a typical day, according to the study, and those who do spend an average of almost two hours in front of the screen. Among all children under 2, the average is 53 minutes a day of television or DVDs — more than twice the 23 minutes a day the survey found children are read to.

And almost a third of children under 2 have televisions in their bedrooms, a substantial increase from 2005, when the Kaiser Foundation found that 19 percent of children ages 6 months to 23 months had them. In families with annual incomes under $30,000, the new study found, 64 percent of children under 8 had televisions in their rooms, compared with 20 percent in families with incomes above $75,000.

Computers are common as well: about 12 percent of children 2 to 4 use them every day, and 24 percent at least once a week, the study found; among those 5 to 8, 22 percent use a computer daily, 46 percent more than once a week. On average, the children who use computers started doing so at age 3 ½.