A certain computer has a memory of $1M$ words, and each word is $32$ bits long. Each

instruction is $32$ bits long and is consisted of an opcode field, a register address field to specify one of $32$ registers, and a memory address field.

a$.$ How large must the register field be$?$

b$.$ How large must the address field be$?$

c$.$ How many different opcodes can be supported by this format?

Show your reasoning to receive partial credit.