Convert the following expressions from infix to reverse Polish (postfix) notation.

1. X * Y + W * Z - V * U
2. W * X + W * (U * V - Z)
3. (W * (X + Y / (U * V)))/(U * (X + Y))
4. ((X+Y)*Z -(X-Y)*Z)

The memory unit of a computer has 1 M words of 32 bits each. The computer has an instruction format with 4 fields: an opcode field; a mode field to specify 1 of 15 addressing modes; a register address field to specify 1 of 16 registers; and a memory address field. Assume an instruction is 32 bits long. Answer the following:

1. 1. How large must the mode field be?
   2. How large must the register field be?
   3. How large must the address field be?
   4. How large is the opcode field?
2. 

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