Triangular Numbers
The triangular number of n is calculated by adding up all the numbers below (and including) n. So if n=5 then the triangular number = 5+4+3+2+1 = 15. The concept dates back to the 5th century BC. Each term is given by the formulae n(n+1)/2. More information on the Triangular Numbers can be found at Wikipedia. |
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Two functions are used:
- Count down function to decrement n.
- Adder function, to add successive terms into S.
Operation
Clear register S. Enter binary value of n and start the train from the station. When the train returns and halts, the nth triangular number can be read from the output register S.
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| Click layout to pause/run train | Click points to switch 0/1 | Click start circle to reset train/points |
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Lazy points switch between upper 0 or lower 1 branch lines Trains arriving on a branch line switch the point to that line |
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Sprung points allow branch line trains to join the main line All main line trains go straight ahead and never 'branch off' |
Notes
- If the nth term exceeds 31, register S overflows and the train returns to the lower station platform as an error. This should not happen as the maximum value for n=7 is 28. Possibly register S was not cleared before calculation began.
- To obtain the correct result, the value of n is added to register S first. This creates an extra 'add 0' calculation at the end.
- The original value of n is 'lost' as the register counts down.
See alternative version of triangular number using a comparator.