An engineering office has a master directory containing 16 GiB of files.
On Monday, Tuesday, Wednesday, and Thursday, users modify or create exactly 512 MiB of data each day.
The IT department needs to calculate the difference in storage required over these 5 days (Sunday to Thursday) for two backup plans:
- Plan A: Perform a full backup every day.
- Plan B: Perform a full backup on Sunday, followed by daily incremental backups.
Let's calculate the total backup storage needed for both plans and determine the total storage savings in GiB.
- Convert all units to a common base:
Recall that Edexcel uses binary prefix factors where 1 GiB=1024 MiB1\text{ GiB} = 1024\text{ MiB}1 GiB=1024 MiB.
Convert the daily incremental change from MiB to GiB:
Daily change=512 MiB1024 MiB/GiB=0.5 GiB
\text{Daily change} = \frac{512\text{ MiB}}{1024\text{ MiB/GiB}} = 0.5\text{ GiB}
Daily change=1024 MiB/GiB512 MiB=0.5 GiB
- Calculate the total storage for Plan A (Daily Full Backups):
A full backup copies all files (16 GiB) every day. Over 5 days (Sunday, Monday, Tuesday, Wednesday, Thursday):
Total Storage (Plan A)=5×16 GiB=80 GiB
\text{Total Storage (Plan A)} = 5 \times 16\text{ GiB} = 80\text{ GiB}
Total Storage (Plan A)=5×16 GiB=80 GiB
-
Calculate the total storage for Plan B (Sunday Full + Incremental):
- Sunday (Full Backup): 16 GiB
- Monday (Incremental): 0.5 GiB
- Tuesday (Incremental): 0.5 GiB
- Wednesday (Incremental): 0.5 GiB
- Thursday (Incremental): 0.5 GiB
Add these together to find the sum:
Total Storage (Plan B)=16 GiB+(4×0.5 GiB)=16 GiB+2 GiB=18 GiB
\begin{aligned}
\text{Total Storage (Plan B)} &= 16\text{ GiB} + (4 \times 0.5\text{ GiB}) \\
&= 16\text{ GiB} + 2\text{ GiB} \\
&= 18\text{ GiB}
\end{aligned}
Total Storage (Plan B)=16 GiB+(4×0.5 GiB)=16 GiB+2 GiB=18 GiB
- Calculate the storage space saved by choosing Plan B:
Subtract Plan B's total from Plan A's total:
Storage Saved=80 GiB−18 GiB=62 GiB
\text{Storage Saved} = 80\text{ GiB} - 18\text{ GiB} = 62\text{ GiB}
Storage Saved=80 GiB−18 GiB=62 GiB