A floppy disk for a computer stores information by magnetizing small regions of the disk. For a typical floppy disk, estimate the area of the disk that corresponds to a single bit of information. (Remember: the storage capacity of a disk is usually given in bytes where 1 byte = 8 bits.)

Solution

Using the first digit of my thumb to measure, I find that a typical floppy disk is about 2.5 inches on a side. This is about (2.5 in) x (2.54 cm/in) or about 6 cm. I know that there is a circular disk inside so it has a radius of about 3 cm. This implies an area of πR² = about 3 x 3 cm x 3 cm or about 30 cm². The floppies I use hold 1.44 MB of information. This is 1.44 x 10⁶ bytes = 1.44 x 10⁶ bytes x (8 bits/byte) = about 10⁷ bits. These bits are distributed over an area of 30 cm² (= 30 x 10^-4 m² = 3 x 10^-3 m²) so, assuming that each bit has its own space and there is no overlap, each bit must occupy a space of (3 x 10^-3 m²) / (10⁷ bits) = 3 x 10^-10 m². If we think of this as a tiny square, it has dimensions Sqrt(3) x 10^-5 m or about 15 micrometers on a side.

Page last modified September 9, 2004: G12