 First, we add the numbers in the rightmost column. Recall that
1 plus 1 adds to 10_{2}, so we can
add the first pair of 1s together, and mark a carry in the next
column.

1
0111
0110
1101
0101
+ 1110

 Now we cross out these 1s since their value is represented
by the carry. The sum of the remaining digits in the first column
is 1, so we write 1 below this column.

1
0111
0110
1101
0101
+ 1110
1

 The second column has two pairs of 1s, so we cross out the first
pair of 1s and mark a carry in the next column to represent these
values.

11
0111
0110
1101
0101
+ 1110
1

 Then we cross out the second pair of 1s and mark another carry
in the next column. Now only zeros remain in this column, so we
write 0 below it.

1
11
0111
0110
1101
0101
+ 1110
01

 The third column has seven 1s, so we cross out three pairs of
1s, and mark three carries in the next column to represent them.
An unpaired 1 remains, so we write it below this column.

1
11
111
0111
0110
1101
0101
+ 1110
101

 Adding the fourth column generates two carries. Since there
is no fifth column, we will create one with all zeros and mark
the carries above it. Next we write the unpaired 1 below the fourth
column.

1
111
1111
00111
00110
01101
00101
+ 01110
1101

 Finally, adding the two carries in the last column gives us
10_{2}, so we write this below the
column, and we have our answer of 101101_{2}.

1
111
1111
00111
00110
01101
00101
+ 01110
101101
