same table, enabling every possible four-digit number to be represented by 4 of the 10 rods. A set of 20 rods, consisting of two identical copies of Napier's 10 rods, allows calculation with numbers of up to eight digits, and a set of 30 rods can be used for 12-digit numbers. Multiplication The simplest sort of multiplication, a number with multiple digits by a number with a single digit, is done by placing rods representing the multi-digit number in the frame against the left edge. The answer is read off the row corresponding to the single-digit number which is marked on the left of the frame, with a small amount of addition required, as explained in the examples below. When multiplying a multi-digit number by another multi-digit number, the larger number is set up on the rods in the frame. An intermediate result is produced by the device for multiplication by each of the digits of the smaller number. These are written down and the final result is calculated by pen and paper. To demonstrate how to use Napier's bones for multiplication, three examples of increasing difficulty are explained below. Example 1 – multiplication by a small single-digit number The first example computes . Napier's bones for 4, 2, and 5 are placed into the board, in sequence. These bones show the larger figure which will be multiplied. The numbers lower in each column, or bone, are the digits found by ordinary multiplication tables for the corresponding integer, positioned above and below a diagonal line. (For example, the digits shown in the seventh row of the 4 bone are , representing .) In the example below for , the bones are here depicted as red (4), yellow (2), and blue (5). The left-most column, preceding the bones shown coloured, may represent the 1 bone. (A blank space or zero to the upper left of each digit, separated by a diagonal line, should be understood, since , , , etc.) A small number is chosen, usually 2 through 9, by which to multiply the large number. In this example the small number by which to multiply the larger is 6. The horizontal row in which this number stands is the only row needed to perform the remaining calculations and may now be viewed in isolation. For the calculation, the digits separated by vertical lines (i.e. paired between diagonal lines, crossing over