DIGITAL COMPUTERS — McCORMICK 289 



sometimes also called a "routine." The first colmnn indicates tlie 

 storage location of the instructions and the data used in the problem. 

 The column "Instruction or number" indicates the contents of each 

 of these storage locations. The "Remarks" column is given merely 

 to assist humans in understanding what is being done ; the computer 

 makes no use of it. A thorough grasp of the sequence of computer 

 operations used in solving the compomid-interest problem is essential 

 to the understanding of digital computers. 



Table 1 also shows how instructions can have the same form as 

 numbers used as data and hence are interchangeable with data. Thus 

 a computer can do aritlunetic operations on its instructions, an interest- 

 ing and useful characteristic of digital computers. 



The above example also illustrates the different manner in which 

 a computer and a human would solve a problem. The most important 

 difference is the extreme detail of the instructions that must be given 

 to the computer, and especially the manner in which these instruc- 

 tions must be stated in order to use the limited number of operations 

 that a computer can perform. Contrast this with the instructions 

 that one would give to a human to do the same job. Even if the 

 calculation of compound interest had to be explained, it would not be 

 necessary to go into such detail to insure that just 20 sets of calcula- 

 tions were made. It will also be noted that many of the operations 

 are concerned with the manipulation of data (going to and from 

 storage, etc.) rather than with the calculations themselves. These 

 "bookkeeping" or "redtape" operations occupy a considerable portion 

 of the program and of the time used in solving the problem. This 

 applies also, however, to the use of a calculator for solving a problem. 

 In a computer it is more obvious, as the instructions for these opera- 

 tions have the same general form as the instructions for doing the 

 arithmetic itself. 



THE PARTICULAR ARITHMETIC OF COMPUTERS 



Aside from manipulation of data and decisionmaking, the essential 

 operations of a computer are simple arithmetic. Since we all know 

 how to add, subtract, multiply, and divide, it may be of interest to 

 know how computers perform these functions. Generally their 

 method differs from that of humans not only in the number system, 

 but also in details of all arithmetic operations. 



Binary numbers. — Most modern digital computers use a binaiy num- 

 ber system rather than the familiar decimal system. There are only 

 2 marks, and 1, instead of 10 different marks, through 9. Each 

 position on either side of the binary point (corresponding to the 

 decimal point) is a power of 2. This is illustrated by table 2, which 

 shows the binary equivalent of decimal digits through 9. The right- 



