When Masayoshi Son, the billionaire Japanese technology investor, solidified his control over his SoftBank internet conglomerate last month, he told shareholders he still wanted to “work on a few more crazy ideas.”

One of those ideas materialized on Monday, when SoftBank unveiled an audacious $32 billion deal to acquire ARM Holdings, the British semiconductor designer. The deal — one of the biggest of the year — would give the Japanese company control of a firm whose chip designs can be found in most of the world’s mobile gadgets, from iPhones and drones to a growing array of smart devices and appliances for the home.

The deal is the first major cross-border transaction in Britain since it voted to exit the European Union last month. Worries over the impact to the British economy have weakened the value of the country’s currency and made it cheaper for foreign companies like SoftBank to hunt for deals there. Compared with this same time in 2015, for example, pound-denominated assets are 30 percent cheaper for buyers holding yen.

For SoftBank, the deal signals another reinvention, this time with a major bet on a future filled with interconnected devices. While major technology companies see a future in smart thermostats and toasters, the technology has not yet become widely available. At the same time, global sales of smartphones have slowed, showing the mobile future has limits.