Hello ,i am struggling to know why i missed this question,would you please solve

Question

Hello ,i am struggling to know why i missed this question,would you please solve it so i can learn.Thank you Define p(z) as the polynomial p(r) (r 2)(r 5)(z 8). (A) What is the smallest numbcr ni such that at least one of the solutions of p(r) 0 has an ni-bit unsigned binary representation? (5 points (B) What is the smallest number n2 such that all three of the solutions of p(z) 0 have n2-bit unsigned binary representations? 15 points] i o l o (C) hat is the smallest number na such that at least one of the solutions of p(r) o has an na-bit two's complement presentation? 15 points (D) What is the smallest number n4 such that all three of the solutions of p(r) 0 have n4-bit two's complement representations? [5 points

Explanation / Answer

solutions of the polynomial = -2, 5, 8

a) Unsigned integers out of these: 5 and 8.

and 5 is the smallest positive.

5 in binary = 101 which is 3 digits long.

Hence n1 = 3.

b) 8 in binary = 1000

Hence, n2 = 4.

c) -2 can be represented using just 2 bits in twos complement system.

Since -2 in twos complement = 11.

Hence, n3 = 2

d) 8 will require the most number of bits in twos complement.

8 = 1000

Also, the most significant bit needs to be 0 for twos complement positive number.

Hence, 8 = 01000 which is 5 bits.

Hence, n4 = 5.

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