10011 base 2
x 111 base 2
------- XOR -------
10011
xor 111
-------
10100
To multiply binary numbers, follow these steps:
Step 1: Write the two binary numbers one below the other, aligning them on the right side.
```
10011 base 2
x 111 base 2
```
Step 2: Start multiplying from the rightmost digit of the second binary number (the multiplier) by each digit of the first binary number (the multiplicand).
In this example, we start with the rightmost digit of the multiplier, which is 1.
Step 3: Multiply the leftmost digit of the multiplicand by the current digit of the multiplier and write the result below, aligned with the current digit of the multiplier.
```
10011 base 2
x 111 base 2
________________
10011 base 2 (Step 3)
```
Step 4: For each subsequent digit of the multiplier, shift the multiplicand one place to the left and multiply it with the current digit of the multiplier. Write the result below, aligned with the current digit of the multiplier.
```
10011 base 2
x 111 base 2
________________
10011 base 2 (Step 4)
00000000 base 2 (Shifted left once)
10011000 base 2 (Shifted left twice)
________________
```
Step 5: Add all the partial products together. The final result is the sum of the partial products.
```
10011 base 2
x 111 base 2
________________
+ 10011 base 2
+ 00000000 base 2
+ 10011000 base 2
________________
11111111 base 2 (Step 5)
```
Therefore, the product of 10011 base 2 and 111 base 2 is 11111111 base 2.