184 



CONVERSION OF NUMBERS TROM ONE SCALE TO ANOTUEB. 



on the second, only the value of r\ the other letters repre- 

 senting unknown quantities: whence, as there are several 

 unknown quantities, and only one equation, it is evident, 

 ' that there ar®;, in, an algebraical point of view", various va- 

 lues of a', b\ c', d', &c., as also of m, that will establish this 

 equality; but the forms being limited to a certain number 

 of digits, less than r', only one possible answer can be ob- 

 tained, and this is best effected independently of any alge^ 

 braical consideration. 

 Numbers ea- There is no difficulty in converting a number from any 

 ed^'^?"the'"* other scale of notation into our own, for we have only to ex-^ ' 

 scale to which press the numbers by means of the foregoing formula, and 

 then collect the value of the separate terms. 



Thus, to transform the number expressed by 74671, in 

 the duodenary scale, into the decimal notation. 



Here 74671 = 12* 7 + 12'.4 + 12*.6 f 12.7 + 1, also 



we are ac- 

 customed. 

 Example 1. 



And 12*7 := 



145152 



12'.4 = 



6912 



12*.(> = 



864 



12.7 = 



84 



1 



1 



therefore 74671 ~ 



153013 



«xa,rap{e 2. Again, convert 3441 from the senary to the decimal scale. 



First 3441 = 6'.3 + 6*.4 + §A + 1. 



and 6'.3 = 64S 



6*.4 =: 144 



6.4= 24 



1 = 1 



riierefore 3441 



817 



Examples. Convert 10101 10 from the binary to the decimal scale of 



notation. 



Here lOlOllO = 2* + + 2* + + 2* + ? + = 86, 

 so that 10101 1 Oj in the binary scale, is expressed by 86 in the 

 commou notation. 



