After solemnly paying his respects at the memorial dedicated to victims of the Boston Marathon bombing, British Prime Minister David Cameron traveled this morning to MIT’s storied Media Lab, where he shared laughs with budding inventors and entrepeneurs.

“So how many different bits are there to the media lab?” Cameron asked as he stepped into the robotics laboratory and shook hands with professor Cynthia Breazeal.

“How many different — different bits? ... How many different groups?’’ Breazeal asked, apparently trying to figure out if Cameron meant bits in the computer sense or in the sense of “parts.”

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“There are 27 now,’’ Breazeal said, referring to the lab’s 27 research groups.

Cameron then witnessed a demonstration of doctoral candidate Kenton Williams’s project, AIDA, which stands for Affective Intelligent Driving Agent, a personal navigation robot for vehicles that is capable of “social interaction” with the driver.

The robot greeted the prime minister by name and even chuckled in the demonstration, drawing a hearty laugh from Cameron.

Cameron toured the lab to learn more about how the school combines innovation with entrepreneurship.

He sat on a plush couch for about 15 minutes with several students, graduates and staff.

“It’s much easier for him to understand ... when we introduce him to students who do this every day, who have these incredibly impressive projects that come out of the labs and we join people across campus, the business school students, the engineering school students, and they work together,’’ said Fiona Murray, faculty director for the Martin Trust Center for MIT Entrepreneurship.