The carry-over ( English carry ) is a term from mathematics and stands for the number of characters in a particular division with arithmetic operations with numbers represented by a value system are presented. In the usual calculation of numbers in the decimal system , one speaks of the transfer of tens .
In a number system with place values, numbers are represented by number signs , in which the symbolizing digits are assigned a place value after the respective place in a digit sequence in addition to their digit value. Two numbers and thus each have a number sign with consecutive digits,
whereby a certain number of digits is available at each position, which characterizes the respective number system as a basic number or base , for example ten digits in the decimal system. If the numbers represented in this way ( -adic) are to be linked to one another by an arithmetic operation , for example the numbers and are added, one has to proceed in places. Then, at the location of a transfer , arise if the intermediate result of the linking of each item and greater than or equal , and thus a multi-digit sequence of numbers. The digits of the surplus places from are then linked with those of the places to from and .
If the range of numbers is limited, arithmetic overflows can occur with addition or subtraction .
If you add the numbers 195 and 107 in decimal representation, you get two carry-overs (shown here in red):
The addition results in the first calculation step to a result that can not be specified by the present digit numbers stock: . Therefore, the digit lowest position in this case will be entered at this point and transmit a digit higher position on the appropriate place, in this case, the as carry-over to the next position. The second calculation step gives . But at this point the carryover still has to be taken into account and counted. again provides a two-digit result and another as a carry over, which results in added .
This method is also used to add in other number representations, such as the dual :