# Operation

At the start all registers show zero, the crank is in the adding position (down), the counter inversion switch is up (the counter counts counts positively) and the register clear handle (ring sticking out) is at the right.

To operate the calculator:

- At the front, slide the red and black sliders up or down on the input register to set an input number.
- Click the crank handle in either the top or front view to make it perform a single revolution, this will add the number of the input register to the result register, and will add one to the counter register. The crank only turns in clockwise sense.
- Click the cap in the front view at the left or the right to make the cap turn by one position, or click one of the small position numbers to move the cap to that position (only positions 1 to 8 are possible). The cap lifts, turns and then drops again. This shifting is used for multiplication and division.
- Click the crank in its axle on either view to make it go up or down. When it is up a red ring shows to warn you that the machine now subtracts the input number from the result (internally it actually still adds, but adds the ten's complement).
- In the top view, click one side of the clearing handle to clear the register on the side you clicked. The handle will then go to rest at the other position between the result and the counter registers. You can clear both registers at once by clicking the clearing handle in the front view. There is no way to clear the input register except by sliding all sliders up to their zero position.
- Click the counter inversion switch to set it to its down position (a red warning dot appears to the right of the counter register in the synoptic view). The counter now subtracts one at each revolution. This is used in division.

# The Four Arithmetic Operations

In the four sections below, “Machine Ready” means: (1) clear all the registers, (2) put the cap in position 1 (to the very left) (3) put the crank in its down position and (4) the counter inversion switch in its up position.

## Addition

We will add the numbers 123, 456 and 789.

- Machine ready
- Set 123 on the input register by sliding the slider 3 (red) to the position where 1 shows above it, slider 2 to position2 and slider 1 to position 3. The number 123 shows in the input register on the front vies and also the input register in the synoptic view.
- Turn the crank once by clicking its handle in either the front or top view. The number 123 shows in the result register (it was added to the already present 000).
- Set the input register sliders to show 456 in the input register.
- Turn the crank once. 456 is added to the result register, showing 579.
- Set the input register to 789.
- Turn the crank, the result is 1368.

Note that the counter register shows 3 because the crank was turned 3 times, but this has no importance in simple additions.

## Addition

We will subtract 432 from 987.

- Machine ready
- Set 987 on the input register.
- Turn the crank once. The number 987 shows in the result register.
- Set 432 on the input register.
- Pull the crank up (to show its red ring) by clicking on its axle, it will now subtract.
- Turn the crank once. 432 is subtracted from the result register, showing 555.

Note that the counter register shows 0 because the crank was turned 1 time in its down position and one time in its up position: 1-1=0, but again this has no importance in simple subtractions.

## Multiplication

We will multiply 1234 by 32. Notice the similarity with the procedure you used at school.

- Machine ready
- Set 1234 on the input register.
- Turn the crank twice. The number 1234 is added 2 times to the result register, showing 2468 and the counter shows 2.
- Turn the cap one position to the right by clicking it on its right side (the cap lifts, turns and comes down again).
- Turn the crank three times. The number 1234 is added three times but one position to the left, which you can interpret as 12340 being added 3 times or 1234 being added 30 times. The result is 39488 and the counter shows 32.

The counter now shows a significant number: 32, the multiplicator of 1234.

### Trick

We will multiply 1234 by 98. Using the same method as above we would turn the crank 8 times and then 9 times or a total of 17 times. But we can do much better:

- Machine ready
- Set 1234 on the input register.
- Lift the crank to show the red ring.
- Turn the crank twice. The number 1234 is subtracted 2 times from the result register, showing 999999999997532 and the counter shows 99999998.
- Turn the cap two positions to the right, 3 is above the cap position indicator.
- Push the crank down again to hide the red ring and make it add again.
- Turn the crank once. The number 123400 (cap position 3!). The result is 120932 and the counter shows 98.

We turned the crank only 3 times. The trick consists of subtracting instead of adding as soon as the digit to multiply by exceeds 6, then adding once at the next cap position.

## Division

We will divide 6543 by 37. Again notice the similarity with the procedure you used at school.

- Machine ready
- Set the cap as far to the right as possible, e.g. by clicking on the small number 8 at the bottom of the cap, or by clicking the cap's right side until this extreme position is reached. This puts result digit 15 above input register digit 8.
- Set 6543 on the input register, but instead of using sliders 4 through 1, use sliders 8 through 5.
- Turn the crank once. The result register shows 654300000000000.
- Clear the counter register by clicking the ring in the top view on the side of the white counter register. The result remains, the counter is 0.
- Set 37 on the input register at sliders 8 and 7, put sliders 6 and 5 back to 0.
- Click the counter inversion switch, it will slide down.
- Pull the crank up to show its red ring. Turning the crank will now subtract, but the counter will count up because of the position of its switch.
- Turn the crank once. That subtracts the 37 from the 65 (first two digits) and leaves 284300000000000 in the result, 1 in the counter. We can't subtract another 37.
- Turn the cap one position to the left, this puts the input 37 now under the 84 of 284300000000000.
- Turn the crank until you can no longer subtract 37, i.e the two-digit number in the result register just above the 37 becomes smaller than 37. If you go one turn too far then a 9 will appear to the left; in that case recover by pushing the crank down, turning once and lifting it again. You should now have 025300000000000 in the result and 17000000 in the counter.
- Turn the cap another position to the left and repeat the previous point. Do this until the cap reaches its end position. You should now have 000000029000000 in the result and 17683783 on the counter.

The result is of course not 17683783 but 176.83783. The problem is to know where the decimal point is. The real machine has some separator indicators and there are procedures to place them so that one of them indicates the decimal point. However, those are a finer points and not the object of the simulator at this time (2019-04).