Editing Addition (section)

=== Non-decimal ===
{{main|Binary addition}}
Addition in other bases is very similar to decimal addition. As an example, one can consider addition in binary.<ref>Dale R. Patrick, Stephen W. Fardo, Vigyan Chandra (2008) ''Electronic Digital System Fundamentals'' The Fairmont Press, Inc. p. 155</ref> Adding two single-digit binary numbers is relatively simple, using a form of carrying:
: 0 + 0 → 0
: 0 + 1 → 1
: 1 + 0 → 1
: 1 + 1 → 0, carry 1 (since 1 + 1 = 2 = 0 + (1 × 2<sup>1</sup>))
Adding two "1" digits produces a digit "0", while 1 must be added to the next column. This is similar to what happens in decimal when certain single-digit numbers are added together; if the result equals or exceeds the value of the radix (10), the digit to the left is incremented:
: 5 + 5 → 0, carry 1 (since 5 + 5 = 10 = 0 + (1 × 10<sup>1</sup>))
: 7 + 9 → 6, carry 1 (since 7 + 9 = 16 = 6 + (1 × 10<sup>1</sup>))

This is known as ''carrying''.<ref>P.E. Bates Bothman (1837) ''The common school arithmetic''. Henry Benton. p. 31</ref> When the result of an addition exceeds the value of a digit, the procedure is to "carry" the excess amount divided by the radix (that is, 10/10) to the left, adding it to the next positional value. This is correct since the next position has a weight that is higher by a factor equal to the radix. Carrying works the same way in binary:

   {{brown|1 1 1 1 1    (carried digits)}}
     0 1 1 0 1
 +   1 0 1 1 1
 —————————————
   1 0 0 1 0 0 = 36

In this example, two numerals are being added together: 01101<sub>2</sub> (13<sub>10</sub>) and 10111<sub>2</sub> (23<sub>10</sub>). The top row shows the carry bits used. Starting in the rightmost column, {{nowrap|1=1 + 1 = 10<sub>2</sub>}}. The 1 is carried to the left, and the 0 is written at the bottom of the rightmost column. The second column from the right is added: {{nowrap|1=1 + 0 + 1 = 10<sub>2</sub>}} again; the 1 is carried, and 0 is written at the bottom. The third column: {{nowrap|1=1 + 1 + 1 = 11<sub>2</sub>}}. This time, a 1 is carried, and a 1 is written in the bottom row. Proceeding like this gives the final answer 100100<sub>2</sub> (36<sub>10</sub>).