All of the computer-related museums and exhibits I'm aware of seem to only cover the history of computing machinery, but nothing on topics of computer science.
You are involved in the creation of a new Museum of Computing, chartered to educate, entertain, and inspire the general public in a wide variety of computing/computer science/communication/mathematics topics. Though history and celebrity can be part of the exhibits, this is not a history museum. Instead, visitors learn about timeless concepts that enable computing, from the hardware layer on up. Budget is not specified but ideas should be durable and practical for high volumes of visitors in permanent installations, with minimal staffing/disposable materials similar to the world's best science centers.
What exhibits would you include?