Around 1945, who developed the idea of a stored program computer that was to hold programs and data in a memory and then data would move between the memory and the processor?

The correct answer is John Von Neumann.

Around 1945, John Von Neumann, a Hungarian-American mathematician and computer scientist, pioneered the concept of the stored-program computer — an architectural design that became the foundation of virtually all modern computers. This concept is often referred to as the Von Neumann Architecture.

Before Von Neumann's idea, early computing machines were largely fixed-function devices. They had to be physically rewired or reconfigured to perform different tasks, making them inflexible and slow to adapt. Von Neumann proposed a revolutionary shift in thinking: instead of hardwiring instructions into the machine, both the program (instructions) and the data should be stored together in the same memory unit.

The key principles of the Von Neumann Architecture can be broken down as follows:

1. Single Shared Memory: The computer uses one unified memory space to store both the instructions (program) and the data the program operates on. This was a radical departure from earlier designs.

2. Sequential Instruction Execution: The processor (CPU) fetches instructions one at a time from memory, decodes them, and then executes them — a process known as the Fetch-Decode-Execute cycle.

3. Data Movement Between Memory and Processor: Data flows back and forth between the memory and the CPU as needed. The CPU reads data from memory, processes it, and writes results back to memory.

4. Binary Representation: All instructions and data are represented in binary (0s and 1s).

Von Neumann formally described this architecture in his landmark 1945 document, the "First Draft of a Report on the EDVAC", where he outlined the design for the EDVAC (Electronic Discrete Variable Automatic Computer). This report cemented his place in computing history.

Now, let's briefly clarify why the other options are incorrect for this specific achievement:

- Alan Turing was a brilliant mathematician who conceptualized the theoretical "Turing Machine" and contributed enormously to computation theory and code-breaking, but he is not credited with the stored-program computer architecture.

- Tim Berners-Lee is the inventor of the World Wide Web (around 1989–1991), which is a completely different contribution made decades later.

- Charles Babbage was a 19th-century inventor who designed the Analytical Engine and Difference Engine — mechanical computing devices from the 1800s, long before the concept of electronic stored-program computers.

Therefore, John Von Neumann is the correct answer, as he is the individual who, around 1945, formally developed and described the idea of a stored-program computer where both programs and data reside in memory, and data moves between the memory and the processor during execution. His architectural model remains the standard blueprint for computers to this day.