Carry (arithmetic)

In elementary arithmetic, a carry is a digit that is transferred from one column of digits to another column of more significant digits. It is part of the standard algorithm to add numbers together by starting with the rightmost digits and working to the left. For example, when 6 and 7 are added to make 13, the "3" is written to the same column and the "1" is carried to the left. When used in subtraction the operation is called a borrow. Carrying is emphasized in traditional mathematics, while curricula based on reform mathematics do not emphasize any specific method to find a correct answer. Carrying makes a few appearances in higher mathematics as well. In computing, carrying is an important function of adder circuits.

In elementary arithmetic, a carry is a digit that is transferred from one column of digits to another column of more significant digits. It is part of the standard algorithm to add numbers together by starting with the rightmost digits and working to the left. For example, when 6 and 7 are added to make 13, the "3" is written to the same column and the "1" is carried to the left. When used in subtraction the operation is called a borrow. Carrying is emphasized in traditional mathematics, while curricula based on reform mathematics do not emphasize any specific method to find a correct answer. Carrying makes a few appearances in higher mathematics as well. In computing, carrying is an important function of adder circuits. 7 + 9 = 16, and the digit 1 is the carry. The opposite is a borrow, as in −1 47 − 19 ---- 28 Here, , so try , and the 10 is got by taking ("borrowing") 1 from the next digit to the left. There are two ways in which this is commonly taught: The ten is moved from the next digit left, leaving in this example in the tens column. According to this method, the term "borrow" is a misnomer, since the ten is never paid back. The ten is copied from the next digit left, and then 'paid back' by adding it to the subtrahend in the column from which it was 'borrowed', giving in this example in the tens column.

Higher mathematics

Kummer's theorem states that the number of carries involved in adding two numbers in base p is equal to the exponent of the highest power of p dividing a certain binomial coefficient. When several random numbers of many digits are added, the statistics of the carry digits bears an unexpected connection with Eulerian numbers and the statistics of riffle shuffle permutations. In abstract algebra, the carry operation for two-digit numbers can be formalized using the language of group cohomology. This viewpoint can be applied to alternative characterizations of the real numbers.

References

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