explain to me how to Multiply in the indicated base
14
5
2
5
________
To multiply in a base other than the usual base 10, you follow a similar process as you would in base 10.
Here's an example:
Let's multiply 14 (base 2) by 5 (base 2).
To do this, we first write the numbers vertically, aligning the ones digits (rightmost) and the twos digits (left adjacent to the ones digits) vertically.
```
14
x 5
------
```
Next, we multiply the ones digit of the second number (5) by the first number (4) and write the result underneath.
```
14
x 5
------
20
```
Since we are in base 2, this result (20) is not valid. We need to convert it to base 2.
To convert, we divide the result (20) by the base (2) and write the remainder as the rightmost digit. The quotient will be the left digit.
In this case, 20 divided by 2 is 10.
```
14
x 5
------
10
```
Next, we multiply the twos digit of the second number (5) by the first number (4) and add it to the previous result. We use the carry from the previous step if necessary.
```
14
x 5
------
10
14
------
```
We add the two results together.
```
14
x 5
------
10
14
------
70
```
To convert the final result (70) to base 2, we divide it by 2 and convert the remainder and quotient.
```
14
x 5
------
10
14
------
70 (base 10)
100 (base 2)
```
So, 14 (base 2) multiplied by 5 (base 2) is equal to 100 (base 2).