Binary Numbers

Binary Numbers

COUNTING SYSTEMS UNLIMITED . . . Since you have been using the

10 different digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 all your life, you may wonder how it is possible to count and do arithmetic without using all 10. Actually, there is no advantage in using 10 counting digits rather than, say,

8, 12, or 16. The 10-digit system (called the decimal system, since the word "decimal" means "based on 10") probably came into universal use because man first started to count by using his fingers, and there happen to be 10 of them. 

To see how to count by using other than 10 digits, notice how we count in the ordinary decimal system. We represent a number higher than 9, the highest digit, by a combination of two or more digits. The number next after 9 is 10, and then 11, etc. After we reach 99, the highest number that can be written with two digits, we start using three digits. The number next after 99 is 100, and then comes 101, etc.

Now let's try counting in the octal system. "Octal" means "based on eight^"; that is, we use only the eight digits 0, 1, 2, 3, 4, 5, 6, and 7. The digits 8 and 9 are not used. So now what do we do after we have counted to 7? Since we have used up all the symbols we are permitted to use, we write 10 as the next number and then comes 11 and so on up to 17.  After 17 comes 20.