If you have a storage device with a capacity of 16 gigabytes, how many 2 kilobyte files can you fit in that device, given that 1 KB equals 1024 bytes?

A 16 gigabyte device holds 2 to the power 34 bytes, and each 2 kilobyte file is 2 to the power 11 bytes, giving 2 to the power 23 files.

16 gigabytes equal 2 to the power 4 times 2 to the power 30 bytes, which is 2 to the power 34 bytes.

A 2 kilobyte file equals 2 times 1024 bytes, which is 2 to the power 11 bytes.

Dividing 2 to the power 34 by 2 to the power 11 subtracts the exponents to give 2 to the power 23.

2 to the power 25 and higher overcount because they assume larger capacity or smaller files than stated.

2 to the power 23 is 8388608, so over eight million such files fit.