Assume an instruction set that uses fixed 20 bit instruction length operands are 8 bits in length. There are P two operand instructions and Q zero operand instructions. Find the maximum number of one operand instruction that can be supported.Correct answer is '4096'. Can you explain this answer?

Question

Answer

Given:
- Instruction set uses fixed 20-bit instruction length
- Operands are 8-bits in length
- P two-operand instructions
- Q zero-operand instructions

To find:
- Maximum number of one-operand instructions that can be supported

Solution:

In a fixed 20-bit instruction length, we need to determine the number of bits required for each instruction type (two-operand, zero-operand, and one-operand) to calculate the maximum number of instructions that can be supported.

Determining bits required for two-operand instructions:
- Each two-operand instruction requires an opcode and two 8-bit operands.
- Since the instruction length is fixed at 20 bits, the opcode will require 20 - 8 - 8 = 4 bits.
- The remaining 8 bits are used for the two operands.

Determining bits required for zero-operand instructions:
- Each zero-operand instruction requires only an opcode.
- Since the instruction length is fixed at 20 bits, the opcode will require 20 - 8 = 12 bits.

Determining bits required for one-operand instructions:
- Each one-operand instruction requires an opcode and one 8-bit operand.
- Since the instruction length is fixed at 20 bits, the opcode will require 20 - 8 = 12 bits.
- The remaining 8 bits are used for the operand.

Calculating the maximum number of instructions:
- The maximum number of instructions for each type can be calculated using the formula 2^n, where n is the number of bits for that instruction type.
- For two-operand instructions: 2^4 = 16
- For zero-operand instructions: 2^12 = 4096
- For one-operand instructions: 2^12 = 4096

Answer:
The maximum number of one-operand instructions that can be supported is 4096.

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