Brand new human and penguin cars have all zeros displayed on the odometer.

After travelling 1 mile both display

So a 1 in this first column means 1 mile in both cars.
After travelling another mile, the humans display shows

However, as we saw at the start, the penguin doesn't have a 2.
So he resets the first column to zero and puts a 1 in the next column.

He says to himself, "a 1 in this second column is worth 2 in decimal".

They both drive another mile.
The humans car displays 3.

Since the penguin has driven the same mile, he puts a 1 in the first column, which we know is worth 1 mile in both cars.

They drive another mile.
The humans car shows 4

The penguin has to reset the first two columns to zero and poke a 1 in the third

He says, " a 1 in the third column is the worth 4 in the decimal system."
So we can correctly guess that a 1 in the fourth column indicate decimal 8

and a 1 in the next is worth 16, and so on.

So when the odometer shows 1111

the car has travelled 8+4 +2 +1 =15 decimal miles.

So adding up in penguin is
0+0=0
0+1=1
1+0=1
1+1= zero and carry 1 = 10

Write the numbers from nought to fifteen, decimal, in penguin.

Penguin counting is the same as BINARY COUNTING.

Binary is used in digital electronic systems, where they have only two values of voltage.