Imagine if we had only two fingers instead of ten. Would we still use Decimal counting, base-10, zero to nine? Or we would naturally use two digits: zero and one to count: binary numeral system. The following shows some examples of binary numbers (indicated with subscript $_2$ ) and their Decimal counterparts.

At first sight, the binary system might look confusing. However, the arithmetic operations on the binary number are essentially the same as we have on a Decimal one: we still have carry-over in summation and borrowing in subtraction.

The same applies to multiplication. First, let's try to do simple multiplication on decimal numbers:

Here, we can see that in column 3, we have
$9+9+9+1=28$

and carry over the "extra digit" 2 to the next decimal place.

Let's try the same on binary numbers:

Again, in column 3, we have $1+1+1+1=100_2$ . What we didn't see in the example of Decimal numbers above is: Here, we need to carry over the additional digits in $100_2$ to the next and the following binary places: $1$ to column 5 and $0$ to column 4.

## Bonus

In Python, we can represent binary numbers by prefixing `0b`

to the numbers. So, for the example above, we have:

```
>>> 0b1111 * 0b111
105
```

Use the `bin()`

function to convert a Decimal to a binary representation:

```
>>> bin(105)
'0b1101001'
```

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