Step 1: Start from the basic building block.
In computing, memory sizes are built on powers of two rather than powers of ten, because everything is addressed in binary. The smallest common unit above the byte is the kilobyte, defined as $1\text{ KB} = 2^{10}$ bytes, which is 1024 bytes.
Step 2: Scale up one more level.
A megabyte is 1024 kilobytes, so we multiply two powers of two together, $1\text{ MB} = 1024 \times 1024$ bytes $= 2^{10} \times 2^{10}$ bytes.
Step 3: Combine the exponents.
Multiplying same-base powers means adding exponents, so $2^{10} \times 2^{10} = 2^{20}$ bytes, which works out to 1,048,576 bytes.
\[ \boxed{2^{20}\text{ bytes}} \]