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 to specify the register?

$2$

$4$

$6$

$7$

$8$

$9$

$10$

$11$