It reminds me about the
decimal number system. What might be the logic behind the implementation of odometer’s
functionality?

It has five digits. Each
digit can take numbers from 0 to 9. Each digit gets incremented by one number
starting from ‘0’ up to ‘9’ and returns back to ‘0’ after ‘9’. Each digit
follows a cycle of 10 numbers (‘0’ to ‘9’ and back to ‘0’). When a digit
reaches 9, and in the next instance, when it moves to ‘0’, its adjacent digit (digit
at its immediate left) gets incremented by 1. This logic seems okay for all the
digits except for the left most one as it doesn’t have a digit to its left. For
the extreme left digit, when the turn comes that it moves from 9 to 0, all the
other four digits also change to ‘0’ (by that time all those digits show 9’s),
such that the meter gets reset and all-zeroes figure appears. It can be
explained in a better way like this: When the magic figure 99999 appears on the
meter, the next turn is initiated from the right most digit. The right most digit changes from ‘9’ to ‘0’ and
initiates movement of second-right digit from ‘9’ to ‘0’, which triggers
third-right digit to change to ‘0’, which very action triggers fourth-right
digit to change to ‘0’ and all this cascading effect triggers finally the
fifth-right (or left-most) digit to change to ‘0’. In all, the range of the
meter is from ‘00000’ to ‘99999’.

That’s fine. But the odometer
continues to haunt me. It reminds me about the frequency with which each digit
changes. In the meter’s overall journey from 00000 to 99999, how many times does the
left-most digit change? What about the right-most digit?

The key lies in the very
fact that “when each digit completes its full turn of

**10**levels (0-to-9) and changes from 9 to 0, its immediate-left digit changes by**1**level”. Here I stress upon the usage of numbers**10**and**1**. I can say it in the other way like this: “By the time a digit turns up**1**level, its immediate-right digit turns by**10**levels”. So if the frequency of a digit is ‘f’ then the frequency of its immediate right digit is ‘10f’.
Now let us start with the
left most digit. By the time meter runs from 00000 to 99999, the left most
digit runs through its full turn (ie, from 0 to 9) by one time. So if we
define ‘frequency’ as ‘number of times a digit changes through’, the frequency of
left most digit can be taken as ‘

**10’**. From then on we can easily calculate the frequencies of other successive digits by simply going for successive 10-multiples. The frequency of second-left digit is 10*10=**100**, that of third-left digit is**1000**, that of fourth-left digit is**10000**and that of fifth-left (or right-most) digit is**100000**.
If all is well, by the
time my bike completes ‘99999’ kilometres of journey, the right most digit of odometer
completes ‘

**100000**’ turns.
When you go for next ride
and when you casually look at the odometer, I hope it would not make you think
about all this and that and go crazy.

*Happy bike riding...*

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