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.

$16.$ What is the largest unsigned binary number that can be accommodated in one word of memory?

$2^8-1$

$2^12-1$

$1^15-1$

$2^16-1$

$2^32-1$

$2^64-1$

$2^128-1$

$2^256-1$