DIGITAL COMPUTERS — McCORMICK 



293 



Table 5. — Coniflement representation for negative numbers 



Number 



5 



4 



3 



2 



1 







Counter 



.. 0005 



.. 0004 



.- 0003 



-. 0002 



.- 0001 



.- 9999 



Number 



-1 



-2 



-3 



-4 



-5 



Counter 

 -- 9998 

 .- 9997 

 .. 9996 

 .- 9995 

 .. 9994 



Table 6. — Counter column illustrates how complements can be used for handling 



negative numbers 



Multiplication. — Most computers do not multiply as such, that is, 

 they do not use multiplication tables. They multiply by a process of 

 repeated addition much as calculators do. The product of 3,514 by 

 7,59G could be obtained by adding 7,596 for a total of 3,514 times, but 

 this would be a tedious process. However, by combining left shift 

 operations (which are the equivalent of multiplying by 10 in a decimal 

 machine or by 2 in a binary machine) with add operations, the number 

 of additions required for multiplication can be considerably reduced. 



The details of how such a multiplication could be done are given 

 in table 7. Assume that the multiplier 3,514 is initially in columns 

 2 through 5 and that the multiplicand 7,596 is added in columns 6 

 through 9. Each time the multiplicand is added, the number in col- 

 umn 1 is reduced 1. When the number in column 1 is the whole 

 accumulator is shifted one position to the left and the process repeated. 

 The 18 steps involved in this particular multiplication should be noted 

 in detail. In this example only 3 + 5 + 1 + 4 or a total of 13 additions 

 would be required. 



Division. — Computer division also is generally done in a manner 

 analogous to methods used in calculators. It involves successive 



