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.

What is the maximum allowable size for memory?

$32$K

$64$K

$128$K

$256$K

$512$K

$1024$K

$2048$K

$4096$K