30 Information Storage and Neural Control 



three examples, the well-known fact that positive numbers are 

 easily represented by a pattern of binary digits, that is to say, 

 by a pattern of "zeros" and "ones." (Binary digits are commonly 

 called bits, for short.) 



Before continuing, it is necessary to recall that negative numbers 

 also have representations in terms of a pattern of bits. To demon- 

 strate this let us discuss methods for negative number representa- 

 tion inside a computer. The following systems are currendy used: 

 [1] Signed absolute values 



[2] Complements with respect to some integral power of the 

 base 



[3] Complements with respect to one less than some integral 

 power of the base. 



The first method is simple — the machine contains the absolute 

 value of each number stored, with an indication of its sign. The 

 second and third methods involve number representation modulo 

 B'' and modulo (^^-1), respectively, where B is the number base, 

 and the machine registers are assumed to hold k digits. 



To illustrate system [2], let /: = 9 and assume a decimal machine. 

 Thus, if we use the symbol = to mean "is represented by," then 



126 « 000 000 126 

 and 



-126 « 999 999 874, 

 since 



-126 = 999 999 874 (mod 10'). 

 Using system [3] we have 



-126 « 999 999 873, 

 since 



10' - 1 = 999 999 999, 

 and 



-126 = 999 999 873 (mod 999 999 999). 



System [3] is sometimes called the "nines complement" system 

 when B is ten. This is motivated by the fact that one merely takes 

 a digitwise complement with respect to nine in forming 999 999 873 

 as the negative representation of 126. System [2] is called the 



