A digital computer has memory unit with the size of $16$ bits. The instruction set consists of $50$ different operations. All instructions have an operation code part $($opcode$)$ and an address part $($allowing for only one address$).$ Each instruction is stored in one memory unit. a$)$ How many bits are used for the address part of the instruction? b$)$ What is the last $($maximum$)$ address for a memory location?