A processor with 16 general purpose registers uses a 32-bit instruction format. The instruction format consists of an opcode field, an addressing mode field, two register operand fields, and a 16-bit scalar field. If 8 addressing modes are to be supported, the maximum number of unique opcodes possible for every addressing mode is ________

Let us determine the bit allocation for the 32-bit instruction format:

1. Scalar field:$16\text{ bits}$

2. Register operand fields: There are 2 register fields. Since there are 16 general-purpose registers, each register field requires:

   $$\log_2(16) = 4\text{ bits}$$

   For two register fields: $2 \times 4 = 8\text{ bits}$.

3. Addressing mode field: To support 8 addressing modes:

   $$\log_2(8) = 3\text{ bits}$$

4. Opcode field:

   $$\text{Opcode bits} = 32 - (16 + 8 + 3) = 32 - 27 = 5\text{ bits}$$

With 5 bits allocated to the opcode, the maximum number of unique opcodes possible is:

Thus, the maximum number of unique opcodes possible for every addressing mode is 32.