Things are actually much simpler in the world of binary multiplication since multiplying by a single digit is as simple as copying the number or inserting 0. The algorithm we will use multiplies only unsigned binary numbers, and in fact only multiplies two 8-bit numbers to form a 16-bit product. Thus, the upper 8 bits of the two numbers we multiply must be 0.

These numbers are traditionally called the multiplier and the multiplicand. They form a product, which can be at most 16 bits long. This is true of any number system: the number of digits in the product can be at most twice the number of digits in the multiplier or multiplicand, if they are the same length.