This is particularly easy for multiplication by 2 since the carry digit cannot be more than 1.

She is always seen carrying Digit's unnamed baby cousin in her arms.

Namely, the sequence of carry digits is the Farey sequence.

Add the two hundreds-digits, and to their sum add the carry digit if there is one.

Then, if there is a carry digit (superscripted, under the line and in the tens-column), add it to this product.

The sum of six and two is eight, but there is a carry digit, which added to eight is equal to nine.

The Prince William County third-grader did not stack the numbers and carry digits from one column to the next, the way generations have learned.

In the addition algorithm the tens-digit of the sum of a pair of digits is called the "carry digit".

If none of the two numbers has a hundreds-digit then if there is no carry digit then the addition algorithm has finished.

If there is a carry digit (carried over from the tens-column) then write it in the hundreds-column under the line, and the algorithm is finished.

The tens-column so far contains only one digit: the tens-digit of the multiplicand (though it might contain a carry digit under the line).

An observation due to Hayyim Selig Slonimski concerning the sequence of carry digits in a multiplication table.

If the sum of the tens-digits (plus carry digit, if there is one) is less than ten then write it in the tens-column under the line.

If the sum has two digits then write down the last digit of the sum in the hundreds-column and write the carry digit to its left: on the thousands-column.

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.

If the multiplicand has a hundreds-digit, find the product of the multiplier and the hundreds-digit of the multiplicand, and to this product add the carry digit if there is one.

Write the "carry digit" above the top digit of the next column: in this case the next column is the tens-column, so write a 1 above the tens-digit of the first number.

The CARRY digit follows the truth table for an AND gate, while the SUM digit follows the truth table for an EXOR gate.

This is in contrast to lattice multiplication, a distinctive feature of which is that the each cell of the rectangle has its own correct place for the carry digit; this also implies that the cells can be filled in any order desired.

The tens-digit of the first number is 5, and the tens-digit of the second number is 7, and five plus seven is twelve: 12, which has two digits, so write its last digit, 2, in the tens-column under the line, and write the carry digit on the hundreds-column above the first number:

To put it another way, we are taking a carry digit from the position on our right, and passing a carry digit to the left, just as in conventional addition; but the carry digit we pass to the left is the result of the previous calculation and not the current one.