$28.$ The memory unit of a computer has $256$ K words of $32$ bits each. The computer has an instruction format with four fields: an opcode field; a mode field to specify one of seven addressing modes; a register address field to specify one of $60$ registers; and a memory address field. Assume an instruction is $32$ bits long. Answer the following:

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

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

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

d$.$ How large is the opcode field?