b) Consider the following Figure 1. S 0 1 2 3 4 5 D w N Y S 0 1 2 3 4 5 6 7 8 w Y LOGICAL MEMORY PHYSICAL MEMORY Figure 1: Logical and physical memory page-to-frame allocation i) Construct a Page Table as a memory map between logical memory with physical memory and backing store based on Figure 1. (6 marks) ii) Update the Page Table after the following operations has been done by the operating system. Page 1 from Logical Memory has been terminated. Page 3 was swap out from Page 6 in the Physical Memory. Page 2 was swap in into Frame 8 in the Physical Memory (3 marks) c) Consider the following page reference string as state below: 00 2 83 2 10 2 11 8 0 2 1 By using the following page replacement algorithm, trace the number of page faults if the given allocated memory is 3 frames. Show your work for each. i) First in First Out Algorithm (6 marks) ii) Optimal Algorithm (6 marks)