A digital computer has a memory unit with $32$ bits per word. The instruction set consists of $200$ different operations. All instructions have an operation code part $($opcode$)$ and two address fields: one for a memory address and one for a register address. This particular system includes $120$ general$-$purpose, user$-$addressable registers. Each instruction is stored in one word of memory.

How many bits are needed for the opcode?

$4$

$8$

$16$

$18$

$20$

$22$

$24$

$32$