Q.Convert the following into bytes:

Digital storage units are based on powers of 2, specifically $2^{10}$ (1024). This is because computers operate using binary digits (bits), and the smallest addressable unit of memory is typically a byte, which consists of 8 bits. Larger units are formed by multiplying by 1024.

Let's convert the given values into bytes:

a) 2 MB

To convert Megabytes to bytes, we multiply by $2^{20}$.

$2 \text{ MB} = 2 \times 2^{20} \text{ bytes}$

$2 \text{ MB} = 2^1 \times 2^{20} \text{ bytes}$

$2 \text{ MB} = 2^{21} \text{ bytes}$

b) 3.7 GB …

To convert digital storage units, we need to understand the hierarchy and the conversion factor between them. In computing, these units are based on powers of $2$, specifically $2^{10}$, which is $1024$. This is because computers operate using binary (base-2) systems.

Here's the standard hierarchy:

• $1 \text{ Byte} = 8 \text{ bits}$
• $1 \text{ Kilobyte (KB)} = 1024 \text{ Bytes}$
• $1 \text{ Megabyte (MB)} = 1024 \text{ Kilobytes (KB)}$
• $1 \text{ Gigabyte (GB)} = 1024 \text{ Megabytes (MB)}$
• $1 \text{ Terabyte (TB)} = 1024 \text{ Gigabytes (GB)}$
• $1 \text{ Petabyte (PB)} = 1024 \text{ Terabytes (TB)}$

To convert a larger unit to a smaller unit, you multiply by $1024$ for each step down the hierarchy.

(a) 2 MB to Bytes

To convert Megabytes to Bytes, we need to go through Kilobytes:

$1 \text{ MB} = 1024 \text{ KB}$

$1 \text{ KB} = 1024 \text{ Bytes}$

So, $1 \text{ MB} = 1024 \times 1024 \text{ Bytes} = 1048576 \text{ Bytes}$.

Now, for $2 \text{ MB}$:

$2 \text{ MB} = 2 \times (1024 \times 1024) \text{ Bytes}$

$2 \text{ MB} = 2 \times 1048576 \text{ Bytes}$

$2 \text{ MB} = 2097152 \text{ Bytes}$

(b) 3.7 GB to Bytes

To convert Gigabytes to Bytes, we need to go through Megabytes and Kilobytes:

$1 \text{ GB} = 1024 \text{ MB}$

$1 \text{ MB} = 1024 \text{ KB}$

$1 \text{ KB} = 1024 \text{ Bytes}$

So, $1 \text{ GB} = 1024 \times 1024 \times 1024 \text{ Bytes} = 1073741824 \text{ Bytes}$.

Now, for $3.7 \text{ GB}$:

$3.7 \text{ GB} = 3.7 \times (1024 \times 1024 \times 1024) \text{ Bytes}$

$3.7 \text{ GB} = 3.7 \times 1073741824 \text{ Bytes}$ …