Questions $(3$ points$/$question$)$:

Show your work, don$$t just list the answer. Only the answer will result $0$ point.

$1.$ Convert the following binary number into decimal.

$10111001$

$2.$ Imagine a number system based on six digits, $0,1,2,3,4,5.$ How many possible values will

this system have if the imaginary computer is a $7-$bit system.

$3.$ Assume the following data in a $32-$bit system $($spaces every $8$ bits for readability$).$ Write this $4-$

byte word in big endian format and in little endian format.

$10100001011011001001011100001001$

$4.$ Write $-12$ in each of the following three formats assuming $8$ bits:

a$)$ Sign magnitude

b$)$ One$$s complement

c$)$ Two$$s complement including sign extension

$5.$ Show how $-78\mathrm{.}5$ would be stored in IEEE format.

$6.$ Given the following number stored in IEEE format, determine its decimal value.

$11000011111000000000000000000000$

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