Question

A machine has a 32-bit architecture with 1-word long instructions. It has 24 registers and supports an instruction set of size 40. Each instruction has five distinct fields, namely opcode, two source register identifiers, one destination register identifier, and an immediate value. Assuming that the immediate operand is an unsigned integer, its maximum value is___.

Hint:

To design instruction formats, allocate bits logically for each field and calculate remaining bits for operands like immediate values. Use \(\lceil \log_2(n) \rceil\) to determine the required bits.

Answer 1

Correct Answer: 2047

To determine the maximum value of the immediate operand in a 32-bit instruction set, we follow these steps: Each instruction is 32 bits long. It includes the following fields: opcode, two source register identifiers, one destination register identifier, and an immediate value. Let's determine the number of bits required for each field:

• Opcode: The instruction set size is 40, requiring ⌈log₂(40)⌉ = 6 bits.
• Registers: There are 24 registers, needing ⌈log₂(24)⌉ = 5 bits each for the two source and one destination registers (totaling 15 bits).
• The remaining bits are for the immediate value: 32 - 6 (opcode) - 15 (registers) = 11 bits.

The largest unsigned integer that can be represented with 11 bits is 2¹¹ - 1 = 2047.