K comes from the Greek word kilo which means a thousand. The Greeks would likewise show million as M, short for Mega. So if we stay consistent with the Greek abbreviations, then billion would be shown as a letter G (Giga). Think of your computer expressing bytes of memory as kilobyte, megabyte, or gigabyte.

In late Latin and the early Romance period the unvoiced velar, represented by C, became palatalized before front vowels, and in the 12th century K was reintroduced as a substitute for C to represent the velar before front vowels since C did duty for both the velar and palatal in such cases and confusion was thus liable ...

K was brought into the Latin alphabet with the name ka /kaː/ to differentiate it from C, named ce (pronounced /keː/) and Q, named qu and pronounced /kuː/. In the earliest Latin inscriptions, the letters C, K and Q were all used to represent the sounds /k/ and /ɡ/ (which were not differentiated in writing).