Charlotte Deutsch, who will be 2 years old next month, has a look of pure delight as she swipes the screen of her mother’s old iPhone, and finds a picture of herself.

“Baby Chacha!” she crows, swiping again to encounter another treasure. “Dada!”

On the new iPhone — the one her mother actually uses — her big sister, Izzy, 4, is utterly intent on “Dora’s Ballet Adventure,” her tiny thumb tapping away at the stars and arrows.

The iPhones, loaded with 20 children’s apps and some 1,200 photographs, are among the girls’ favorite playthings. “The little one loves to go through the pictures and name who’s in them, see her grandma and her nanny,” said their mother, Tina Deutsch, a former nursery school teacher. “The older one loves the games, and taking pictures. She loves the clicking sound, and if it’s blurry, she knows how to delete it.”

As adults turn, increasingly, to mobile devices like tablets, Kindles, and iPhones, their children — even the smallest ones — are doing so as well, according to a new study, “Zero to Eight: Children’s Media Use in America, 2013” by Common Sense Media, a San Francisco-based nonprofit organization that examines children’s use of technology, and rates children’s apps, games and Web sites.