Calculations with an adding machine.


This description of calculations is based on adding machines like the comptometer. But it can also be applied to other adding machines, if you change the text a little bit.

Addition

Addition is quite straightforward; to add two numbers we might merely depress first the keys corresponding to the digits of the first number and then the digits of the second number. The result of the addition is shown in the result register. Some adding machines only has keys with digits from 1 to 5. A number greater than 5 can be typed by two successive depressions of lower keys. For example 8 can be added by depression of 5 and 3.
    Example: 85607 + 439 = ? on a machine with the keys from 1-5:
  1. Zeroise the result registers.
  2. Type 55505
  3. Add 30102. The result register shows 85607.
  4. Add 435 and finely 4.

Substraction

Substraction on a machine of this type is performed by addition of complements. The complement of a number is defined as the number which gives with addition the next power of ten as result. For example: the complement of 567 is 433, because 567 + 433 = 1000. The complements have to be determined mentally, but to make this simple, the keys are specially marked. In addition to the normal engravings 1, 2, 3, 4, 5, 6, 7, 8 and 9, there are also small figures: 8 on the 1 key, 7 on the 2 key, 6 on the 3 key, 5 on the 4 key, 4 on the 5 key, 3 on the 6 key, 2 on the 7 key, 1 on the 8 key and 0 on the 9 key. To find the complement of a number it is necessary to consider these small figures and use them instead of the normal large figures. There is an exception for the column at the utmost right. For this column we have to substract 1 first. For example: the complement of 64 (36) can be pressed with the small 6 at the second column from the right and the small 3 (= 4 -1) at the utmost right column.
There are a few special cases which are really covered by the rule, but which are perhaps more easily remembered separately. Since there is no zero key there is correspondingly no key with a small 9 and a 9 in the number whose complement is wanted must be ignored. If there is a zero in the units column this must also be ignored and 1 substracted instead from the tens column. Thus the complement of 940 is found by depressing no key in the hundreds column, the small 3 (actually 6) in the tens column, and no key in the units column.
    Example: 85607 - 439 = ? :
  1. Zeroise the result registers.
  2. Type 85607
  3. Add 99561(large key numbers) or 00438 (small key numbers)
  4. The result register shows 185168.
  5. The really result is 85168.

Multiplication

A multiplication can be carried out by repeated addition. For example 43 * 76 = 3 * 76 + 4 * 760. This can easily be carried out as follow: Press the 6 at the utmost right column and the 7 on the second column from the right at one time. If this is done three times then we have the result of 3 * 76. Then we place our fingers one column to the left (7 on the third column from the right and 6 on the second column from the right) and press the keys 4 times (4 * 760).

Division (with arithmetical complement)

Division is performed by succesive substraction in the same way as you would do a division with penci and paper. The best way to show this is with an example.
    Example: 32723 : 43 = ? :
  1. Zeroise the result registers.
  2. Type 32723
  3. Substract 43 from 327 as you would do with paper and pencil. Substraction goes of course with the complement of 043 and this is 957.
  4. The result register shows 128423, 224123, 319823 415523, 511223 606923 and 702623.
  5. Since 43 > 26 we stop. The substraction is carried out 7 times..
  6. Now we substract 43 from 262 by means of the complement 957.
  7. The result register shows 712193, 721763, 731333, 740903, 750473 and 760043.
  8. Since 43 > 04 we stop. The substraction is carried out 6 times.
  9. Substract 43 from 43 by means of the complement 957.
  10. The result register shows 76100. The result of the division is 761.


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