28 Injormation Storage and Neural Control 



Assume that the number of electronic components required to 

 represent a single digit, base 5, is approximately proportional to 

 B. Thus, a rough estimate of the number of electronic components 

 required to represent n digits, base B, is 



TV = n lu B, 

 where A"i is a constant. 



If B" = P is held fixed, and we wish to find the value of B 

 which minimizes the number of electronic components, N, needed 

 to represent P numbers, we proceed as follows: Since 



i?" = P, 



we can write 



and so 



n In B = In P 

 = /v%. 



cJN _ „ 

 dB - ^^' 



In B • 

 Thus, the number of electronic components needed is 



KsB 



In B • 



DifTerentiating with respect to B yields 



InB - r 



. (In BY' _■ 



Setting this derivative equal to zero gives us 



biB = 1, 

 or 



B = r 



= 2.71828 .... 



For integer values of B the minimum occurs when B = 3, with 

 slightly greater values for B = 2. 



Since tristable devices are almost nonexistent, and bistable devices 

 are plentiful, most engineers choose the binary numeral system 

 rather than the ternary numeral system when they design a 

 machine. 



