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Registers in a CPU are small, fast storage locations that hold instructions and data temporarily during the execution of programs. Their primary function is to facilitate quick access to the data and instructions that the CPU is currently processing. This rapid access enhances the efficiency and speed of computations since registers operate at the same speed as the CPU itself, allowing the processor to perform operations without the latency introduced by accessing slower memory types such as RAM.

While the other options reference important aspects of computer architecture, they do not capture the specific use case of registers. Long-term data storage is typically the role of hard drives or SSDs, while memory allocation is managed by the operating system through structures like heaps and stacks. Executing complex algorithms often requires multiple processing steps and larger data sets that surpass the capacity of registers alone. Thus, option B correctly identifies the critical role of registers in facilitating immediate data and instruction handling during CPU operations.