DIGITAL COMPUTERS — McCORMICK 



291 



A 

 B 



^ C^^AB 



S^ (A + 3)(AB) 



Figure 1. — Logical circuit for binary addition. 



decimal system. For example, the 3-decimal digit number 785 re- 

 quires 10 binary bits 1100010001 for its representation. Thus a binary 

 computer would need to do 3i/^ times as many binaiy operations to be 

 equivalent to decimal aritlmietic. However, this is a small price to 

 pay for the advantages gained. 



Eeferring back to table 3, we note that the conditions under which 

 the swm digit is a 1 can be stated in words as, "when A is a 1 or B is a 

 1 and both A and B are not 1." Similarly, the condition for a 1 in 

 the carry digit is, "when A is 1 and B is 1." The italicized words are 

 important because they show how a binary addition operation can be 

 expressed in words, and^ or^ and not^ which are terms with logical 

 meaning. The basic ideas of and^ or^ and not are familiar to everyone 

 and their use in digital computer adders is the same as in the usually 

 understood concepts of these terms. It is thus possible to draw a 

 logical diagram for binary addition as shown in figure 1. This figure 

 should be compared with the above word statement on binary addition 

 and with table 3. They are equivalent ways of expressing the same 

 thing. 



The exact form of the adder in a digital computer varies from 

 one computer design to another. The and^ or^ and not devices may 

 use vacuum tubes, transistors, or magnetic devices. However, the 

 logic, no matter how implemented, is the same. 



Obviously, the addition operation must be done for eacli pair of 

 digits in the two numbers to be added. Furthermore, in general, it 

 is not simply a matter of adding just two digits together; it is neces- 

 sary also to add the carry digit from the previous less significant 

 addition. Thus a full-adder considers all three inputs. The device of 

 figure 1 is a half -adder since it considers only two inputs. A full adder 

 can be formed by using two half adders. 



