MATHEMATICS 21 



n, in the radix of two, we produce the following 

 result : 



ion 



ion 



ion 

 ion 



0000 

 IOII 



IIIIOOI 



This may be proved to be right by analysing the 

 product and comparing it with a similar analysis of 1 1 

 times ii in the system of the radix 10. 



Radix of 2. Radix of 10. 



1 = 1 I 



I GOO 2 A 8 



10000 2 4 l6 



1 00000 2' 5 32 



1000000 2 64 



IIIIOOI 121 



Now 1111001 is ii multiplied by itself according to 

 the radix of 2. But 121 is also n multiplied by itself 

 according to the radix 10 : 



ii 

 ii 



ii 



ii 



121 



