SAN FRANCISCO — Texas Instruments said Monday that it planned to acquire National Semiconductor for $6.5 billion in a deal that places a big bet on the increasing need to translate the physical world of humans into the digital form of computers and then back again.

Both companies specialize in making “analog” processors, a particular kind of computer chip that converts data from the real world — temperature, light intensity, dust concentrations, shifting magnetic fields — into digital data that a computer can interpret and then back again, if need be, into visual or aural information that a human can understand.

Such chips are critical components in devices like cameras and phones, but they are crucial in a host of other electronic devices and sensors used in industry and medicine. They are frequently custom designed and carry high profit margins compared with commodity computer chips. Demand for the chips has grown as the number of devices needing sensors has grown.

Under terms of the deal, Texas Instruments has agreed to pay $25 a share for National Semiconductor. That is more than a 77 percent premium for National, whose share price closed at $14.07 just before the announcement. In after-hours trading, National’s shares rose almost 73 percent, to $24.30. Texas Instruments shares lost 1.55 percent after hours, to $33.58.