Binary Representation of Information 31 



"tens complement" system when B is ten, since the least significant 

 digit is actually complemented with respect to ten. 



In a nine-digit binary machine using "ones complements," we 

 would have 



[126]ten « 001 111 no, 



and 



[-126]ten « 110 000 001. 



Thus we have reviewed, by means of examples, how both positive 

 numbers and negative numbers may be represented easily by a 

 pattern of bits. 



PROCESSING BINARY INFORMATION 

 INSIDE A COMPUTER 



Let us consider a typical modern high-speed computer which 

 is designed to process binary information in blocks of 48 bits. 

 Such blocks are called words, and we describe such a computer 

 as having a 48 bit word length. These words may be bit patterns 

 representing numbers (we discussed binary representations of 

 numbers in the previous section) or the words may be bit patterns 

 having a non-numerical interpretation. To the machine this is 

 immaterial. 



The repertoire of machine commands for carrying out operations 

 on machine words includes commands for performing the basic 

 arithmetic operations of addition, subtraction, multiplication, and 

 division. More complicated mathematical tasks, such as the ex- 

 traction of square roots, solving algebraic equations, and so on, 

 are accomplished by using a combination of these basic commands. 



In addition to the commands for performing basic arithmetic 

 operations, the machine is capable of executing commands which 

 perform operations of a non-numerical character. These are the 

 commands that make the modern electronic digital computer a 

 versatile information-processing instrument rather than just a 

 high-speed computing instrument. 



We begin our discussion of non-numerical type commands 

 (although some of these may have a numerical interpretation 

 as well) by mentioning the shift cortimands. Consider the bit pattern 

 consisting of ones in the odd numbered positions and zeros in 



