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**
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 k_{1} is either ‘0’ or ‘1’. Equation (2) can be reformulated
as,

(2.3)

(2.4)

Where, and k_{2} is either ‘0’ or ‘1’. Similarly, can be decomposed as,

(2.5)

Where, k_{3}
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 2^{q} where q is an integer.
So at last it can be written as,

(2.8)

In Binary
mathematics, a=2, q=n and k_{n}=x_{n-1}. So equation (8) can be
reformulated as,

(2.9)

(2.10)