Egyptian Mathematics for Multiplication
Derivation:
Consider two
numbers and
, where ‘a’ is the radix. Our aim is to compute the product of two given
numbers as well as execute the division operation between them using the
ancient Egyptian mathematics. The product P can be expressed as,
(2.1)
(2.2)
Where, and k1 is either ‘0’ or ‘1’. Equation (2) can be reformulated
as,
(2.3)
(2.4)
Where, and k2 is either ‘0’ or ‘1’. Similarly,
can be decomposed as,
(2.5)
Where, k3 is either ‘0’ or ‘1’. Putting equation (5) in equation (4), we get,
(2.6)
(2.7)
This will continue until ‘n’ cannot be divisible by 2q where q is an integer. So at last it can be written as,
(2.8)
In Binary mathematics, a=2, q=n and kn=xn-1. So equation (8) can be reformulated as,
(2.9)
(2.10)