To add $0011\;\;1010_{2}+0001\;\;0111_{2}$ we:
 Align the digits vertically
 Add the rightmost column, containing 0 and 1, yielding 1. Because this is less than the quantity that can be represented by a single digit, we have no carry.
 We move to the left, position 1, where we have no carry, a 1 and a 1, yielding 10. Because this is greater than the quantity that can be represented by a single digit, we carry.
 We move to the left, position 2, where we have a carry, a 0 and a 1, yielding 10. Because this is greater than the quantity that can be represented by a single digit, we carry.
 We move to the left, position 3, where we have a carry, a 1 and a 0, yielding 10. Because this is greater than the quantity that can be represented by a single digit, we carry.
 We move to the left, position 4, where we have a carry, a 1 and a 1, yielding 11. Because this is greater than the quantity that can be represented by a single digit, we carry.
 We move to the left, position 5, where we have a carry, a 1 and a 0, yielding 10. Because this is greater than the quantity that can be represented by a single digit, we carry.
 We move to the left, position 6, where we have a carry, a 0 and a 0, yielding 1. Because this is less than the quantity that can be represented by a single digit, we have no carry.
 We move to the left to the final column, where we have no carry, a 0 and a 0, yielding 0. Because this is less than the quantity that can be represented by a single digit, we have no carry.
 Done

position

7

6

5

4

3

2

1

0

carry

0

1

1

1

1

1

0

0

addend

0

0

1

1

1

0

1

0

addend

0

0

0

1

0

1

1

1

sum

0

1

0

1

0

0

0

1

