In the context of MARIE (Machine Architecture that is Really Intuitive and Easy), MAR refers to the Memory Address Register, and AC refers to the Accumulator.

• The MAR in MARIE is responsible for holding the memory address of the data being accessed or stored. It is used to fetch instructions and operands from memory or to store results back into memory. The MAR's purpose is to provide the address to the memory system so that the desired data can be accessed.
• On the other hand, the AC is the primary working register in the MARIE architecture. It holds data that is being manipulated or processed by the CPU. The AC performs arithmetic and logical operations, stores intermediate results, and can be used to hold the final result of a computation.
• The reason why the MAR is only 12 bits wide while the AC is 16 bits wide in MARIE is primarily due to the design choices made in the architecture. The MAR is narrower because it needs to store memory addresses, which are typically smaller than the actual data being manipulated. In MARIE, memory addresses are 12 bits long, allowing a total of 2^12 (4096) memory locations to be addressed.
• On the other hand, the AC is wider to accommodate the data being processed. With a width of 16 bits, the AC can store a wider range of values, including integers, floating-point numbers, or other data types. The extra bits in the AC provide more flexibility for computations and storage of larger values.
• By having a narrower MAR and a wider AC, MARIE strikes a balance between addressing memory efficiently and providing sufficient storage and computational capabilities. The design choices in MARIE reflect the specific needs and constraints of the architecture, aiming for simplicity and ease of understanding rather than maximum performance or versatility.