$1.$We have a computer where a word is just $5$ bits long. Now, you have to do the following arithmetic:

a$)(-9)-5$

b$)(-12)+(-5)$

All decimal, and all in two's complement. Can you show the operations and what the result is$?$ Was there any error?

Now explain the concept of Tmin in two's complement. What would $-$Tmin be$?($Hint: is it Tmax? $0?$ what?$)$

$2.$ Lay out the magic word, OxDEADBEEF, in memory starting from location $0400000,$ for a MIPS computer. How about for an x$86$ computer?

$($Hint: is MIPS little$-$endian or big$-$endian? What about x$86?)$

$3.$ Run the following code in C$,$ and your results. $($Hint: is $>$ in C doing an or a right shift? What is the difference?$)$

A certain machine has $12-$bit instructions and $4-$bit addresses. Some instructions have one address and others have two. Both types of instructions exist in the machine.

a$)$ What is the maximum number of instructions with one address?

b$)$ What is the minimum total number of instructions, assuming the encoding space is completely utilized $($no more instructions can fit$)?$

$($Hint: think of MIPS with its $32-$bit instructions and $5-$bit operand addresses. The same logic applies here $)$