Digital storage devices often use the binary based phone number system suppose you have a USB flash drive with capacity of 8 GB question 1 Express the total storage capacity in bytes given that 1GB is equals to (2 raise to power 30) bytes provide answer in base10

Answer 1

To express the total storage capacity of an 8 GB USB flash drive in bytes, we start with the conversion factor that 1 GB equals \(2^{30}\) bytes.

Given that: \[ 1 \text{ GB} = 2^{30} \text{ bytes} \]

We can calculate the total storage of 8 GB in bytes as follows:

\[ 8 \text{ GB} = 8 \times 2^{30} \text{ bytes} \]

Now, we can express 8 as \(2^3\):

\[ 8 \times 2^{30} = 2^3 \times 2^{30} = 2^{3+30} = 2^{33} \text{ bytes} \]

Next, we need to calculate \(2^{33}\) in base 10. To do this:

\[ 2^{10} = 1024 \]

To find \(2^{30}\), we calculate:

\[ (2^{10})^3 = 1024^3 \]

Calculating \(1024^3\):

\[ 1024 \times 1024 = 1,048,576 \quad (this \ is \ 2^{20}) \]

Now multiplying \(1,048,576\) by \(1024\):

\[ 1,048,576 \times 1024 = 1,073,741,824 \quad (this \ is \ 2^{30}) \]

Finally, we compute \(2^{33}\):

\[ 2^{33} = 2^{30} \times 2^3 = 1,073,741,824 \times 8 = 8,589,934,592 \]

Thus, the total storage capacity of an 8 GB USB flash drive in bytes is:

\[ \text{Total Storage Capacity} = 8,589,934,592 \text{ bytes} \]