20 ELEMENTS OF SCIENCE 



Numbers expressed in the Numbers expressed in the 



radix of 10. radix of 12. 



TOO 84 



144 1 20 (i 2 times 



12) 



1728 1440 



Bui instead of 10 or 12, we might make use of a 

 binary system of notation, that is, we might take 2 as 

 the radix. Then to express numbers according to such 

 a system, an additional figure would have to be added to 

 the right for every increase of 2, as follows : 



Radix of 10. Hadix of 2. 



o 



1 ; I 



2 10 



3 ii 



4 100 



5 ii 



6 no 



7 in 



8 1000 



9 1001 



10 1010 



11 ion 



Thus according to this system every time the symbol 

 one is moved one space to the left, its value is doubled 

 as we see above (in the radix of 2), where 10 is twice i ; 

 100 twice the value of 10, and 1000 twice the value of 

 100. 



If we square (multiply by itself) this last number 



