Final answer:
An accumulator in a 4-bit register system is responsible for temporarily storing data during arithmetic and logic operations, which aids in the processing of sequences of operations in a CPU.
Step-by-step explanation:
The task of an accumulator connected to an adder in a 4-bit register system is to store the data temporarily during arithmetic and logic operations. This is a fundamental component of a central processing unit (CPU) in a computer, which is capable of storing intermediate results of calculations. In the context of the options provided, the best description for an accumulator is option (a): it stores the data temporarily during arithmetic and logic operations. This temporary data storage allows for the subsequent processing of information in a sequence of operations, which is crucial for executing complex calculations and algorithms.