Counting can be done by the sorter, the tabulator, and the collator. The tabulator can print the total count. The tabulator and summary punch wired together can put the total count automatically into another punch card. The sorter shows the count in dials. Adding and Subtracting Adding and subtracting can be done by the tabulator, the calculating punch, and the multiplying punch. In the calculating and multiplying punches, the sum or difference is usually punched into the same card from which the numbers were first obtained. The tabulator, however, obtains the result first in a counter; from the counter, it can be printed on paper or punched into a blank card with the aid of the summary punch. Numbers are handled as groups of decimal digits, and the machines mirror the properties of digits in the decimal system. Negative numbers are usually handled as _complements_ (see Supplement 2). For example, if we have in the tabulator a counter with a capacity of six digits, the number-000013 is stored in the counter as the complement 999987. We cannot store in the counter the number +999987, since we cannot distinguish it from-000013. In other words, if a counter is to be used for both positive and negative numbers, its capacity is actually one digit less, since in the last decimal place on the left 0 will mean positive and 9 will mean negative. Multiplying and Dividing Multiplying is done in the calculating and multiplying punches. In both cases, the multiplication table is built into the circuits of the machine, and the system of _left-hand components_ and _right-hand components_ is used (see Supplement 2). Dividing is done in the calculating punch and is carried out in that machine much as in ordinary arithmetic. By means of an estimating circuit the calculating punch guesses what multiple of the divisor will go into the dividend. Then it determines that multiple and tries it. Rounding Off Rounding off may be done in 3 punch-card machines, the calculating and multiplying punches, and the tabulator. For example, suppose we have the numbers 49.1476, 68.5327, and we wish to round them off to 2 decimal places. The results will be 49.15 and 68.53. For the first number, we raise the .0076, turning .1476 into .15, since .0076 is more than .005. For the second number, we drop the .0027 since it is less than .005. Each of these punch-card machines provides what is called a _5 impulse_ in each machine cycle. When the number is to be rounded off, the 5 impulse is plugged into the first decimal place that is to be dropped, and it is there added. If the figure in the decimal place to be dropped is 0 to 4, the added 5 makes no difference in the last decimal place that is to be kept. But, if the figure in the decimal place to be dropped is 5 to 9, then the added 5 makes a carry into the last decimal place that is to be kept, increasing it by 1, and this is just what is wanted for rounding off. LOGICAL OPERATIONS