Subtraction adds the additive inverse: . On the number line, is a shift three units left from . Reversing the two inputs changes the sign: , so subtraction is generally not commutative. Solving gives the same answer by adding to both sides; the operation preserves equality while undoing the added amount.
In positional subtraction, a higher place supplies one unit of its place value when the current place cannot subtract the requested digit. In binary representation, subtraction of one, a low bit toggles at every operation and the borrow continues through each zero bit, stopping at the first one bit. Thus decrementing a binary counter toggles position exactly when all less significant bits were zero. This is the downward-counting counterpart of a carry propagating through one bits during incrementing.
Articles by others on the same topic
Subtraction is one of the four basic arithmetic operations, alongside addition, multiplication, and division. It involves taking one number away from another. The result of a subtraction operation is called the difference. In a subtraction expression, the number from which another number is taken is called the "minuend," the number that is being subtracted is called the "subtrahend," and the result is known as the "difference.
