GATE2025_CS1_Q27

A partial data path of a processor is given in the figure, where RA, RB, and RZ are 32-bit registers. Which option(s) is/are CORRECT related to arithmetic operations using the data path as shown?

Note: This is a Multiple Select Question (MSQ). One or more options may be correct.

✅ Final Answer:

The correct options are (A), (B), and (C).

🔹 Short Answer:

The datapath uses two multiplexers (Mux_A and Mux_B) to select the inputs for the ALU. Each multiplexer can choose between a register (RA or RB) and an immediate value. This flexibility allows the ALU to receive inputs in any combination: two registers (A), one register and one immediate value (B), or two immediate values (C). Statement (D) is false because it wrongly claims exclusivity.

🔸 Long Answer:

This question requires analyzing the flow of data through the given processor datapath to determine which types of arithmetic operations are possible. The key components are the multiplexers (Mux_A and Mux_B) that control the inputs to the ALU.

Datapath Component Analysis

• ALU Inputs: The Arithmetic Logic Unit (ALU) takes two inputs to perform an operation.
• Mux_A: This multiplexer selects the first input for the ALU. Its sources are the value from register RA and an immediate value.
• Mux_B: This multiplexer selects the second input for the ALU. Its sources are the value from register RB and a different immediate value.

By controlling the "Select" lines of these two multiplexers, we can configure the datapath to perform different types of operations. Let's evaluate each option based on possible Mux configurations.

Analysis of Each Option

1. (A) The data path can implement arithmetic operations involving two registers.
   This requires sending the contents of RA and RB to the ALU.
   • Set Mux_A to select the input from RA.
   • Set Mux_B to select the input from RB.
   The datapath supports this configuration. Therefore, this statement is TRUE.
2. (B) The data path can implement arithmetic operations involving one register and one immediate value.
   This can be achieved in two ways:
   • Config 1: Set Mux_A to select RA and Mux_B to select its immediate value.
   • Config 2: Set Mux_A to select its immediate value and Mux_B to select RB.
   Since the datapath supports these configurations, this statement is TRUE.
3. (C) The data path can implement arithmetic operations involving two immediate values.
   This requires sending two immediate values to the ALU.
   • Set Mux_A to select its immediate value input.
   • Set Mux_B to select its immediate value input.
   The datapath supports this configuration. Therefore, this statement is TRUE.
4. (D) The data path can only implement arithmetic operations involving one register and one immediate value.
   The word "only" makes this a very restrictive claim. It implies that the configurations described in (A) and (C) are impossible. As we have just shown that operations with two registers and two immediate values are possible, this statement is definitively FALSE.

Bibliography:
- Patterson, D. A., & Hennessy, J. L. (2017). Computer Organization and Design: The Hardware/Software Interface. Morgan Kaufmann. (Chapter 4: The Processor).
- Stallings, W. (2016). Computer Organization and Architecture: Designing for Performance. Pearson.

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