290 



ANNUAL REPORT SMITHSONIAN INSTITUTION, 1960 



Table 2. — Table of binary equivalents to decimal numbers 



Decimal 







1 



2 



3 



4 



Binary 

 . 0000 

 . 0001 

 . 0010 

 . 0011 

 . 0100 



Decimal 



5 



6 



7 



9. 



Binary 

 . 0101 

 . 0110 

 . 0111 

 . 1000 

 . 1001 



most binary position indicates the presence (by a 1) or the absence 

 (by a 0) of a 1, the next position the presence or absence of a 2, 

 the next a 4, an 8, and so on. Thus 0111 is 4+2 + 1, or 7; 1001 is 8 + 1, 

 or 9; 1100010001 would be 512 + 256 + 16+1, or 785; 110.011 would be 

 4+2+1/4 + 1/8, or 63/8. 



The reason for using a binary notation system is a practical one. 

 Computers consist of devices which must be very fast and extremely 

 reliable. The electronic devices which best meet these requirements 

 are two-state (bistable) elements. Thus it is possible only to know 

 whether these devices represent one bit of information, that is, either 

 a or 1. For example, whether a certain spot on a magnetic tape is 

 magnetized in one direction or in the other direction, whether a vacuum 

 tube is conducting current or not, a hole is punched in a card or it is 

 not, etc. 



Binary addition. — Another advantage of the binary number sj^stem 

 is that binary arithmetic is quite simple. The binary addition table 

 is given in table 3. The two numbers A and B can each have values 

 of or 1 so that there are only four possibilities to consider. An 

 example of binary addition which uses all four combinations is given 

 in table 4. However, binary representation means that about Sy^ 

 times as many marks are needed to represent a number as with the 



Table 3. — The binary addition table 



Table 4. — Binary addition and decimal equivalent 

 Binary Decimal 



110 

 10 10 



8+4 =12 

 8 + 2 =10 



10 110 



16 + 4+2 = 22 



