When humans first began to count, they used their ten fingers as a basis for numeration. This led to the adoption of the ten-based system into everyday life. Infinately many number systems can be used, but a few stand out as the most practical. These include the two-, eight- and ten-based systems. If humans would switch from a ten-based system to an eight-based system, there would be greater efficiency between humans and machines because of the relationship of the eight-based system to the computer’s two-based system.
Humans rely on a ten-based system, consisting of the coefficients of the powers of ten (Asimov 30). “Our ordinary numbers are simply the ten-based system, working on a series of powerse of ten,” (Asimov 30). To humans, the ten-based system seems just right, having only ten digits to memorize and the ability to reach any number under 10,000 using only four digits (Asimov 34). There is, however, nothing basic or fundamental about ordinary numbers, it is just one of infinately many systems of numeration (Asimov 30).
The two-based system is composed of the exponents of powers of two (Asmimov 21). “Any number at all can be expressed by some combination of 1’s and 0’s” in the two-based system (Asimov 23). This system of numeration is ideal for computers, because the 1’s and 0’s can be represented by an on or off position of a certain switch, which is simplicity itself for teh computer (Asimov 26). In the age of computers that is surrounding us, there is a substantial attraction to the two-based system, although to humans it is an “uncomfortable and unaesthetic mèlange of 1’s and 0’s.” (Asmimov 34).
The eight-based system, based on the successive powers of eight, is closely related to the two-based system (Asimov 34). For intsnace, 1000 in the two-based system is equal to 10 in the eight-based system; or, if you prefer, 23 is equal to 10 81 (Asimov 34). Another benefit to the eight-based system is that a two-based number can be broken into groups of three digits and converted easily to the eight based system once ione memorizes the following table (Asimov 35).
|Two-Based System||Eight-Based System|
For instance, the two-based number, 101111100 can be broken into 101,111,100 and converted to the eight-based number 574 (Asimov 35).
By converting to the eight-based system, greater understanding would exist between man and machine (Asimov 35). It is unimaginable how much faster science and technology would progress (Asimov 35). A switch to a different numeration system at this time, however, is totally impratical (Asimov 35). But just think - “suppose that, origionally, primitive man had learned to count on his eight fingers only and had left out those two awkward and troublesome thumbs,” (Asimov 35).
Asimov, Isaac. Asimov on Numbers. New York: Pocket Books, 1977.