Editing Binary number (section)

=== Subtraction ===
{{further|signed number representations|two's complement}}

[[Subtraction]] works in much the same way:

:0 − 0 → 0
:0 − 1 → 1, borrow 1
:1 − 0 → 1
:1 − 1 → 0
Subtracting a "1" digit from a "0" digit produces the digit "1", while 1 will have to be subtracted from the next column. This is known as ''borrowing''. The principle is the same as for carrying. When the result of a subtraction is less than 0, the least possible value of a digit, the procedure is to "borrow" the deficit divided by the radix (that is, 10/10) from the left, subtracting it from the next positional value.

     *   * * *   (starred columns are borrowed from)
   1 1 0 1 1 1 0
 −     1 0 1 1 1
 ----------------
 = 1 0 1 0 1 1 1

   *             (starred columns are borrowed from)
   1 0 1 1 1 1 1
 –   1 0 1 0 1 1
 ----------------
 = 0 1 1 0 1 0 0

Subtracting a positive number is equivalent to ''adding'' a [[negative number]] of equal [[absolute value]]. Computers use [[signed number representations]] to handle negative numbers—most commonly the [[two's complement]] notation. Such representations eliminate the need for a separate "subtract" operation. Using two's complement notation, subtraction can be summarized by the following formula:

: {{math|1=A − B = A + not B + 1}}