Add the two binary numbers 11102 and 1112.

We have:

• One group of 8 ($1 \times 8 = 8$)
• One group of 4 ($1 \times 4 = 4$)
• One group of 2 ($1 \times 2 = 2$)
• Zero groups of 1 ($0 \times 1 = 0$)

Add these up: $8 + 4 + 2 + 0 = 14$.
So, $1110_2$ is the same as 14.

We have:

• One group of 4 ($1 \times 4 = 4$)
• One group of 2 ($1 \times 2 = 2$)
• One group of 1 ($1 \times 1 = 1$)

Add these up: $4 + 2 + 1 = 7$.
So, $111_2$ is the same as 7.

Now we just add $14 + 7$.
$14 + 7 = 21$.

We need to find which binary place values add up to 21. We'll use the place values: $16, 8, 4, 2, 1$.

• Does 16 fit into 21? Yes. So we use one 16. $21 - 16 = 5$ left over. Binary: 1 (for the $16$s place)

• Does 8 fit into 5? No. So we don't use an 8. Binary: 0 (for the $8$s place)

• Does 4 fit into 5? Yes. So we use one 4. $5 - 4 = 1$ left over. Binary: 1 (for the $4$s place)

• Does 2 fit into 1? No. So we don't use a 2. Binary: 0 (for the $2$s place)

• Does 1 fit into 1? Yes. So we use one 1. $1 - 1 = 0$ left over. Binary: 1 (for the $1$s place)

Putting the binary digits together from left to right (from the $16$s place down to the $1$s place), we get $10101_2$.