In arithmetic, "carry" refers to an essential concept that occurs during addition, particularly when adding multi-digit numbers. When the sum of digits in a given place value exceeds the base of the numbering system, a carry is generated. The excess value is then transferred to the next higher place value. For example, consider adding the two numbers 27 and 58: ``` 27 + 58 ----- ``` 1.
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In positional notation with integer base , a carry transfers units in one position into one unit in the next position during addition. Each such transfer lowers the sum of the numeral digits by .