The beginning of a free-space bitmap looks like this after the disk partition is first formatted$:\: 1000\: 0000\: 0000\: 0000$ (the first block is used by the root directory). The system always searches for free blocks starting at the lowest-numbered block, so after writing file $A,$ which uses six blocks, the bitmap looks like this$:\: 1111\: 1110\: 0000\: 0000.$ Show the bitmap after each of the following additional actions:
- File $B$ is written, using five blocks.
- File $A$ is deleted.
- File $C$ is written, using eight blocks.
- File $B$ is deleted.