This question concerns the field $(256)$

$.$ The modulus is $()=8+4+3++1$

$.$

Please answer the following questions about arithmetic in this field.

a$)$ If $()=6+$

$,$ what is the corresponding hexadecimal representation? Please prepend an $"0$x$"$ on your answer and use lowercase letters $($if letters occur$).$

$0$x$42$

b$)$ If $()=4++1$

$,$ what is the corresponding hexadecimal representation? Please prepend an $"0$x$"$ on your answer and use lowercase letters $($if letters occur$).$

c$)$ Consider the hex byte $009$

$.$ What is the corresponding element of GF$(256)($as a polynomial$)?$

d$)$ Consider the hex byte $07$

$.$ What is the corresponding element of GF$(256)($as a polynomial$)?$