1). In a 1,024-KB segment, memory is allocated using the buddy system. Using Figure 9.26 as a guide, draw a tree illustrating how the following memory requests are allocated:

Request 6-KB

Request 256 bytes

Request 956 bytes

Request 1,500 bytes

Request 70-KB

Next, modify the tree for the following releases of memory. Perform coalescing whenever possible:

Release 256 bytes

Release 956 bytes

Release 1,500 bytes

2). The page table given below is for a system with 16-bit virtual and physical addresses and with 4,096-byte pages. The reference bit is set to 1 when the page has been referenced. Periodically, a thread zeroes out all values of the reference bit. A dash for a page frame indicates the page is not in memory. The page-replacement algorithm is localized LRU, and all numbers are provided in decimal.

page	page frame	reference bit
0	9	0
1	1	0
2	14	0
3	10	0
4	-	0
5	13	0
6	8	0
7	15	0
8	-	0
9	0	0
10	5	0
11	4	0
12	-	0
13	-	0
14	3	0
15	2	0

a. Convert the following virtual addresses (in hexadecimal) to the equivalent physical addresses. You may provide answers in either hexadecimal or decimal. Also set the reference bit for the appropriate entry in the page table.

0xE12C

0x3A9D

0xA9D9

0x7001

0xACA1

b. Using the above addresses as a guide, provide an example of a logical address (in hexadecimal) that results in a page fault.

c. From what set of page frames will the LRU page-replacement algorithm choose in resolving a page fault?