I 



CHAPTER 

 II 



BINARY REPRESENTATION OF 

 INFORMATION 



Robert T. Gregory, Ph.D. 

 INTRODUCTION 



T IS well known that most modern electronic digital computers 

 use the binary representation of numbers internally rather than 

 the more familiar decimal representation, although sophisticated 

 programming systems may allow the computer user to do almost 

 all of his communicating with the machine in decimal. The 

 reason for the fact that binary representation is in common use 

 is explained in the next section. 



It is tiie purpose of this paper to review the binary representation 

 of numbers, including the word structure for a typical binary 

 computer, and to demonstrate some typical machine commands 

 that are available for manipulating patterns of binary digits. It 

 is hoped that this will provide some indication of the extreme 

 versatility of the electr'onic computer as an information processing 

 instrument and will encourage those who have not yet discovered 

 its usefulness to explore its potentialities. 



REPRESENTING NUMBERS INSIDE A COMPUTER 



It is well known to those who design the basic circuits for 

 digital computers that the optimum number base, B, for representing 

 numbers inside a computer, from the standpoint of economy of 

 electronic hardware needed, is, B = 3. To verify this let us recall 

 that the number of numbers that can be expressed using n digits, 

 base B, is B". For example, in the decimal numeral system if 

 n = 3, we can express 10^ numbers 000, 001, . . ., 999. 



27 



