GATE CS 2024 Set 2 Q47 — Machine Instructions and Addressing Modes

To find the maximum number of unique opcodes, we need to determine the size of the opcode field in the $32$-bit instruction format.

Let's calculate the bits required for each field in the instruction:

• Register Operand Fields: The processor has $16$ general-purpose registers. The number of bits required to address one register is: $$\log_2(16) = 4\text{ bits}$$ Since there are two register operand fields, they require: $$2 \times 4 = 8\text{ bits}$$
• Addressing Mode Field: The processor supports $8$ addressing modes. The number of bits required is: $$\log_2(8) = 3\text{ bits}$$
• Scalar Field: Given as $16\text{ bits}$.

The total number of bits occupied by these fields is:

Since the total instruction format is $32$ bits, the remaining bits are allocated to the opcode field:

The maximum number of unique opcodes possible with $5$ bits is: