Adding multiple binary numbers uses the same principles as adding two binary numbers, but we will approach it using a slightly different method.



  1. First, we add the numbers in the rightmost column. Recall that 1 plus 1 adds to 102, so we can add the first pair of 1s together, and mark a carry in the next column.
       1
     0111
     0110
     1101
     0101
  +  1110
  1. 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
  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
  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
  1. 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
  1. 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
  1. Finally, adding the two carries in the last column gives us 102, so we write this below the column, and we have our answer of 1011012.
     1
    111
    1111
    00111
    00110
    01101
    00101
  + 01110
   101101

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