Number-Systems

Question 27

Convert the following numbers in the given bases into their equivalents in the desired bases.
(a) 110.101)₂ = x)₁₀
(b) 1118)₁₀ = y)_H

A	(a) 6.625, (b) (45E)_H

Question 27 Explanation:

(a) 1*2² + 1*2¹ + 0*2⁰ + 1*2^-1 + 0*2^-2 + 1*2^-3
= 4 + 2 + 0 + 0.5 + 0 + 0.125
= 6.625

(b) 1118 mod 16 = E, quotient = 69
69 mod 16 = 5, quotient = 4
4 mod 16 = 4
Writing the mods result in reverse order gives (45E)_H.

Correct Answer: A

Question 27 Explanation:

(a) 1*2² + 1*2¹ + 0*2⁰ + 1*2^-1 + 0*2^-2 + 1*2^-3
= 4 + 2 + 0 + 0.5 + 0 + 0.125
= 6.625

(b) 1118 mod 16 = E, quotient = 69
69 mod 16 = 5, quotient = 4
4 mod 16 = 4
Writing the mods result in reverse order gives (45E)_H.