# Why the Russian peasant method works using binary numbers?

## Why the Russian peasant method works using binary numbers?

Understand why the method works. The Russian peasant method works because it converts the problem into binary (base 2) multiplication, rather than base 10 (which standard multiplication uses).

What is Russian peasant method?

Russian peasant multiplication is an interesting way to multiply numbers that uses a process of halving and doubling without using multiplication operator. The idea is to double the first number and halve the second number repeatedly till the second number doesn’t become 1 .

Was the Russian peasant method used by Russian peasants?

The multiplication algorithm [Wells, p. 44] discussed below is commonly known as the Russian Peasant Multiplication. It is even said that the algorithm “is still used by peasants in some areas, such as Russia.” However, the source of the Russian Peasant designation is unexpectedly murky.

### Why is it called the Russian peasant multiplication?

Since it does not require any form of writing and involves only three operations, pairing off, halving and doubling, which are both easy to carry out and are not troublesome conceptually, the system remained extremely popular with peasants the world over and became known as Russian Multiplication because, until …

Where is Egyptian multiplication used today?

This method is still used in many rural communities in Ethiopia, Russia, the Arab World, and the Near East. The term that we use with Egyptian Multiplication is called Doubling. You take one number and either multiply it by 2 or you add it to itself.

What is Russian method?

In the Russian peasant method, the powers of two in the decomposition of the multiplicand are found by writing it on the left and progressively halving the left column, discarding any remainder, until the value is 1 (or −1, in which case the eventual sum is negated), while doubling the right column as before.

## Can Russian serfs be sold?

Only the Russian state and Russian noblemen had the legal right to own serfs, but in practice commercial firms sold Russian serfs as slaves – not only within Russia but even abroad (especially into Persia and the Ottoman Empire) as “students or servants”.

What is Russian lip filler?

The Russian technique accentuates the cupid’s bow to resemble a heart-shape by injecting additional volume and lift into the center of the lips, while the sides still remain relatively in line with the face. The result is doll-like while still appearing naturally full and plump.

How to multiply two numbers using the Russian peasant method?

Russian peasant method allows us to find the multiplication of two numbers without using multiplication tables. In this method, we divide the numbers, half them and then add them up. Here are the steps to find multiplication using the Russian peasant method.

### How to calculate the efficiency of binary search?

The standard way to analyze the efficiency of binary search is to count the number of times the search key is compared with an element of the array. Moreover, for the sake of simplicity, we will count the so-called three-way comparisons.

Which is the correct way to multiply a binary expression?

1. Dividing X in half repeatedly, ignoring the remainder, gives the coefficients for the binary expression of X. 2. Multiplying the binary expression of X yields a sum of Y times powers of 2. We only need to add the non-zero terms, which correspond to the halved terms of X that are odd.

Can a binary search be implemented as a nonrecursive algorithm?

If they match, the algorithm stops; otherwise, the same operation is repeated recursively for the first half of the array if K < A[m], and for the second half if K > A[m]: Though binary search is clearly based on a recursive idea, it can be easily implemented as a nonrecursive algorithm, too. Here is pseudocode of this nonre-cursive version.