Consider NUM =(X₃​X₂​X1₁X₀​)₁₆​, an arbitrary 4 digit number in base 16 . How many bits do we need for representing a single digit of NUM, e.g. X0​ in base 2 ? (Mark=5%) 4. Using the previous question and the "shift property" show that the direct conversion rule from base 16 to base 2 is correct. More formally, show that: (Mark=15\%)

(X₃​X₂​X1₁X₀​)₁₆​ ​= ((X₃​)₂​​(X​)₂​​(X₁​)₂​(X₀​​)₂​​)₂​