Question

1. an external computer flash drive can hold i gigabyte of data.how many bytes is this?

Explanation:

Step1: Recall the conversion factor

We know that in computer storage, \( 1 \text{ gigabyte (GB)} = 2^{30} \text{ bytes} \) (binary conversion) or sometimes in decimal it is considered as \( 10^{9} \) bytes, but the standard binary conversion for computer storage is \( 2^{30} \). Let's calculate \( 2^{30} \).

Step2: Calculate \( 2^{30} \)

We know that \( 2^{10}= 1024 \) (which is also called a kilobyte in binary terms). Then \( 2^{30}=(2^{10})^{3}\). Substituting \( 2^{10} = 1024 \), we get \( (1024)^{3}\).

Calculating \( 1024\times1024 = 1048576 \), then \( 1048576\times1024=1073741824 \).

Alternatively, if we use the decimal approximation (where \( 1 \text{ GB} = 10^{9} \) bytes for some contexts like hard drive manufacturers), but for computer storage (RAM, flash drives in terms of binary), it is \( 2^{30}=1073741824 \) bytes.

Answer:

If we consider the binary conversion (standard for computer storage), \( 1 \) gigabyte is \( 1073741824 \) bytes. If we consider the decimal conversion (used by some manufacturers), it is \( 1000000000 \) bytes. But the standard binary value for computer data storage is \( \boldsymbol{1073741824} \) bytes.