explain in detail. Assignment:

For each problem, include units where appropriate.

$1.$ Perform the necessary base conversions to complete each row and fill in the table. Make

sure to show the work that supports this. Note that since it is easy to get lost looking at

bit patterns, let$$s get in the habit of writing them in groups of four $($except for the leftmost

group$).$

binary decimal hexadecimal

$1111000$

$35$

$0$xB$4$

$2.$ The $1989$ C standard gives minimums for the integer types. While an int must be at least

two bytes, on modern computers it is typically four bytes. This creates a portability issue.

The $1999$ C standard $($referred to as C$99)$ includes the library stdint.h$.$ This library contains

typedefs for exact$-$width integer types. For example, int$16$ t is a $16-$bit signed integer in the

twos complement representation while uint$32$ t is a $32-$bit unsigned integer.

Complete this table, using base$-10$ values:

number of minimum maximum

variable type bit arrangements value value

uint$8$ t $2560255$

int$8$ t

uint$16$ t

int$16$ t

uint$32$ t

int$32$ t

$3.$ Give the $8-$bit, twos complement binary representation for each of these.

$($a$)$ int$8$ t a $=510$;

$($b$)$ int$8$ t b $=1610$;

$($c$)$ int$8$ t c $=9310$;

$($d$)$ int$8$ t d $=12710$;

$4.$ For each base$-10$ number n below, determine the largest power of $2<=$ n and the minimum

number of bits needed to represent n as an unsigned integer.

n $2$k $<=$ n min bits

$923=84$

$31$

$58$

$100$

$256$