A proposed computer design has 16 bit instructions. The computer should be able to work with a 2 KB byte-addressable memory. There are 8 general purpose registers available. The CPU designer wants the following types of instructions to be supported.

• 3 instructions with a register address and a memory address
• 7 instructions with only a memory address
• 15 instructions with only a register address
• 8 zero-address instructions

Perform the following tasks.

a) Mathematically prove that the proposed design is possible (count the bit patterns).

b) Propose an instruction set design, indicating all the escape opcodes.

c) Based on the above design, provide pseudo code to find out the type of a given instruction