A digital computer has a memory unit with $16$ bits per word. The

instruction set consists of $61$ 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

word of memory.

a$)$ How many bits are used for the address part of the instruction?

b$)$ What is the maximum addressable size of the memory?

c$)$ By considering signed magnitude representation, what is the largest signed binary

number that can be accommodated in one word of memory?