Carry (arithmetic)

The carry ( engl. carry) is a term from mathematics and stands for the number of characters in a particular sub-step in arithmetic operations with numbers that are represented by a place value system. In the usual calculation of numbers in the decimal one speaks so well of tens transfer.

In a number system with point values ​​numbers are represented by numerals in which the symbolizing digits next to their numeric value in each case is assigned in a sequence of numbers after each point, another priority. Two numbers and thus have each a numeral with durchnummerierbaren places

Where at any point a certain number of digits is available that features than basic number or the respective base number system, so the decimal ten digits. If the so ( - adic ) numbers shown now be linked together by an arithmetic operation, such as the numbers and added, so you must act locally. Then, a transfer can occur at the point when the intermediate result of the operation of the various items and greater than or equal to, and thus a multi-digit sequence of numbers. The numbers of surplus places by then with those of the sites linked to and from.

If the number range is limited, it may lead to arithmetic overflow when adding or subtracting.

Example: Addition

If you add up the numbers 195 and 107, arising in decimal representation of numbers as follows two transfers ( shown here in red ):

The addition results in the first calculation step to a result which no longer can be specified with the present -digit numeric stock. Therefore, the lowest digit position, in this case, be entered at this point and transferred one digit higher position on the appropriate location, in this case, the. Than carry to the next position is The second calculation step results. But still the transfer must then be taken into account and are counted at this point. provides continued double-digit earnings and again one as a carry, the results to be counted.

In other representations of numbers, such as the dual, is added with this method:

Related Topics

In information technology, the carry through a carry ( carry bit ) is realized.

• Numeracy