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Question: Consider a file system using the linked allocation method. The file system has 1024 blocks and block numbers require 32 bits to store. The block size is 2 KB. The file system has only one root directory in which we are creating files of the size of 998 bytes. Directories store the file name and starting block. The files created will have a file name with 24 characters. How blocks will the root directory occupy once we created these files? The only options are 8, 7, 3 and 1
In order to calculate how many blocks the root directory will occupy once the files are created, we need to consider the following information: 1. Block size: 2KB (2048 bytes) 2. File size: 998 bytes 3. File name: 24 characters (assuming 1 byte per character) 4. Starting block number: 32 bits (equivalent to 4 bytes) Now, let's calculate the size of a directory entry for each file: Directory entry size = File name size + Starting block number size Directory entry size = 24 bytes + 4 bytes Directory entry size = 28 bytes Now we need to find out how many directory entries can fit in each block: Directory entries per block = Block size / Directory entry size Directory entries per block = 2048 bytes / 28 bytes Directory entries per block ≈ 73 entries The options for the number of blocks are 8, 7, 3, and 1. We need to calculate how many files can be stored in these blocks and if that number can hold all the files when they have a size of 998 bytes. 1 block: Max files stored = 73*1 = 73 files Total storage space = 73 files * 998 bytes = 72,854 bytes 3 blocks: Max files stored = 73*3 = 219 files Total storage space = 219 files * 998 bytes = 218,442 bytes 7 blocks: Max files stored = 73*7 = 511 files Total storage space = 511 files * 998 bytes = 509,978 bytes 8 blocks: Max files stored = 73*8 = 584 files Total storage space = 584 files * 998 bytes = 582,832 bytes Now, to answer the question, we can see that among these options, 3 blocks can hold 219 files and have more than enough storage capacity for the 998-byte files. So, the root directory will occupy 3 blocks.
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