Which of the following represents one billion characters ?

CONCEPT

Digital storage is counted in bytes, and each unit name is built from a prefix that fixes an order of magnitude. Under the SI (decimal) convention that governs these byte-based names, kilobyte denotes 103 bytes, megabyte 106 bytes, gigabyte 109 bytes and terabyte 1012 bytes. The nearby powers of two carry their own IEC names and symbols: kibibyte (KiB) = 210 bytes, mebibyte (MiB) = 220 bytes, gibibyte (GiB) = 230 bytes and tebibyte (TiB) = 240 bytes. Older usage often applied the decimal names to these binary sizes, but each binary unit still sits in the same decade as the decimal unit it shadows, so the prefix alone fixes the order of magnitude either way. Turning a count of characters into a storage unit needs one further fact: how many bytes one character occupies. This classical exam convention assumes a single-byte encoding such as ASCII, in which one character occupies exactly one byte.

APPLICATION

1. State the encoding convention the item relies on: one character is stored in one byte, as in ASCII and the other single-byte encodings. One billion characters therefore occupy 109 bytes.

2. Find the unit whose prefix denotes 109 bytes. That prefix is giga, so 109 bytes is one gigabyte.

3. Test the result against the alternative readings, so that it does not rest on the convention chosen. Reading the unit names in their older binary sense puts the requirement at 109 / 230 = 0.93 of a gibibyte; storing the same text in a fixed two-byte encoding instead of a single-byte one doubles it to 2 x 109 bytes. Both readings stay inside the same decade.

4. Therefore one billion characters is represented by a gigabyte.

CROSS-CHECK

Laying the offered units side by side, with their decimal sizes and the character counts they hold at one byte per character, shows how far each one sits from the requirement:

Only the gigabyte row carries the one billion characters the stem asks for: the kilobyte and megabyte rows fall short by six and by three orders of magnitude, and the terabyte row overshoots by three.