Learn in the textbookBinary Numbers and Radix
DefinitionBinary addition (加算) adds digit by digit from the lowest one up, and whenever a digit's sum reaches 2 or more, it carries 1 into the next higher digit.
ExplanationAdding one digit to another gives 0+0=0, 0+1=1, 1+0=1, and 1+1=10, so a carry appears only for 1+1. When a digit that already received a carry from below becomes 1+1+1, it keeps 1 and also carries 1 upward. Doubling a number shifts the whole thing one digit to the left, and multiplication can be done as an addition of shifted copies.
AnalogyPicture a wallet with a rule: as soon as two coins of the same kind pile up, they are swapped for one coin of the next higher value.
Memory hookBinary 1+1 plays the same role as decimal 9+1: in both, the digit rolls over the moment it passes the largest digit that place can hold.