Ads
related to: multiplying 4 digits by numbers pdf
Search results
Results From The WOW.Com Content Network
The basic principle of Karatsuba's algorithm is divide-and-conquer, using a formula that allows one to compute the product of two large numbers and using three multiplications of smaller numbers, each with about half as many digits as or , plus some additions and digit shifts.
It requires memorization of the multiplication table for single digits. This is the usual algorithm for multiplying larger numbers by hand in base 10. A person doing long multiplication on paper will write down all the products and then add them together; an abacus-user will sum the products as soon as each one is computed.
Some of the algorithms Trachtenberg developed are ones for general multiplication, division and addition. Also, the Trachtenberg system includes some specialised methods for multiplying small numbers between 5 and 13. The section on addition demonstrates an effective method of checking calculations that can also be applied to multiplication.
Multiplication by a positive number preserves the order: For a > 0, if b > c, then ab > ac. Multiplication by a negative number reverses the order: For a < 0, if b > c, then ab < ac. The complex numbers do not have an ordering that is compatible with both addition and multiplication. [30]
For truncation, a certain number of leftmost digits are kept and remaining digits are discarded or replaced by zeros. For example, the number π has an infinite number of digits starting with 3.14159.... If this number is truncated to 4 decimal places, the result is 3.141.
976 + 348 ---- 978 (adding digits column-wise) 976 × 348 ---- 876 (multiplying the digits of 976 by 8) 444 (multiplying the digits of 976 by 4) 333 (multiplying the digits of 976 by 3) ----- 34876 (adding digits column-wise) The concept of lunar arithmetic was proposed by David Applegate, Marc LeBrun, and Neil Sloane. [3]