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Trachtenberg defined this algorithm with a kind of pairwise multiplication where two digits are multiplied by one digit, essentially only keeping the middle digit of the result. By performing the above algorithm with this pairwise multiplication, even fewer temporary results need to be held. Example:
The number that is two times the simple is marked in the two triangles marked × 2. If the number is two digits, the first digit is placed to the left of the main diagonal (marked in red) and the second digit to the right of the diagonal. If the number is a single digit, it is marked to the right of the diagonal; The number that is 3 times the ...
The abacus system of mental calculation is a system where users mentally visualize an abacus to carry out arithmetical calculations. [1] No physical abacus is used; only the answers are written down. Calculations can be made at great speed in this way.
36 represented in chisanbop, where four fingers and a thumb are touching the table and the rest of the digits are raised. The three fingers on the left hand represent 10+10+10 = 30; the thumb and one finger on the right hand represent 5+1=6. Counting from 1 to 20 in Chisanbop. Each finger has a value of one, while the thumb has a value of five.
In arbitrary-precision arithmetic, it is common to use long multiplication with the base set to 2 w, where w is the number of bits in a word, for multiplying relatively small numbers. To multiply two numbers with n digits using this method, one needs about n 2 operations.
Two binary abacuses constructed by Robert C. Good Jr., made from two Chinese abacuses. The binary abacus is used to explain how computers manipulate numbers. [62] The abacus shows how numbers, letters, and signs can be stored in a binary system on a computer, or via ASCII. The device consists of a series of beads on parallel wires arranged in ...
The Korean finger counting system Chisanbop uses a bi-quinary system, where each finger represents a one and a thumb represents a five, allowing one to count from 0 to 99 with two hands. One advantage of one bi-quinary encoding scheme on digital computers is that it must have two bits set (one in the binary field and one in the quinary field ...
A suanpan (top) and a soroban (bottom). The two abaci seen here are of standard size and have thirteen rods each. Another variant of soroban. The soroban is composed of an odd number of columns or rods, each having beads: one separate bead having a value of five, called go-dama (五玉, ごだま, "five-bead") and four beads each having a value of one, called ichi-dama (一玉, いちだま ...
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