## Introduction

When you use your computer or your calculator to do difficult calculations, or when you see your child easily do the following multiplication...

68
x 43
-----------
204
272
-----------
2924

...we have to remember the suffering of the ancient people throughout history to calculate the operations of arithmetic. However, they left us great works certifying that they were geniuses.

History tells us about two operations of multiplication, Ancient Egyptian multiplication and Russian peasants multiplication.

## Ancient Egyptian Multiplication

Here is how 43 is multiplied by 68:

- Start with number 1 in the first column and keep doubling (the first column has powers of two), the largest power of two less than or equal to the first number(43).
- Start with the second number (68) in the second column, keep doubling the number in the second column.
- Subtract the largest power of two less than or equal to the first number(43),

43 - 32 = 11,

subtract the largest power of two less than or equal to the remainder(9),

11 - 8 = 3

repeat,

3 - 2 = 1

repeat until nothing remains,

1 - 1 = 0

Now you see that 43 = 32 + 8 + 2 + 1.
- To get the result, check the numbers in the second column corresponding to 32, 8, 2, 1 and add them.

## Russian Peasants Multiplication

See how 43 is multiplied by 68:

- Write each number at the head of a column.
- Divide the number in the first column by 2, flooring the quotient (drop the remainder), until there is nothing left to divide.
- Keep doubling the number in the second column, until you have doubled it as many times as you divided the number in the first column.
- To get the result, add up all the numbers in the second column that are next to an odd number in the first column.

## Background

To test the previous operations of multiplication, begin a new project with one form, put the following controls on the form:

- Two controls of
`TextBox`

: `txtFirst `

and `txtSecond `

to enter two numbers.
- Two controls of
`CheckedListBox `

for Ancient Egyptian multiplication: `lstEgyptian1 `

and `lstEgyptian2`

.
- Two controls of
`CheckedListBox `

for Russian peasants multiplication: `lstRussian1 `

and `lstRussian2`

.
- Two controls of
`Label `

to print the result: `EgyptianResult `

and `RussianResult`

.
- Three controls of
`Button`

s: `btnEgyptianCalc`

, `btnRussianCalc `

to get the result and `btnExit `

to exit the program.

## About the Code

Fill the first list:

private void FillListEgyptian1()
{
newVlue = 1;
numFirst = Convert.ToInt32(txtFirst.Text);
lstEgyptian1.Items.Clear();
while (newVlue <= numFirst)
{
lstEgyptian1.Items.Add(newVlue);
newVlue = 2 * newVlue;
}
} int

Fill the second list:

private void FillListEgyptian2()
{
numSecond = Convert.ToInt32(txtSecond.Text);
lstEgyptian2.Items.Clear();
lstEgyptian2.Items.Add(numSecond);
for(int i = 1; i < lstEgyptian1.Items.Count; i++)
{
numSecond = numSecond * 2;
lstEgyptian2.Items.Add(numSecond);
}
}

Check numbers at first column:

private void CheckEgyptianNumbers()
{
int newNumber = numFirst;
int i = lstEgyptian1.Items.Count;
do
{
i--;
int binNumber = (int)(lstEgyptian1.Items[i]);
if(binNumber <= newNumber)
{
newNumber = newNumber - binNumber;
lstEgyptian1.SetItemChecked(i, true);
lstEgyptian2.SetItemChecked(i, true);
}
}
while (i > 0);
}

Add numbers to get the result:

private void GetEgyptianMultiplication()
{
long TheResult = 0;
for(int i = 0; i < lstEgyptian2.Items.Count; i++)
{
if(lstEgyptian2.GetItemChecked(i) == true)
{
TheResult = TheResult + (int)(lstEgyptian2.Items[i]);
EgyptianResult.Text = TheResult.ToString();
}
}
}

You can read the code of Russian peasants multiplication.

## Final Words

We must not forget what knowledge the previous generations have given us.

Said Isaac Newton,

"I stand on the shoulders of my predecessors".

Thanks to Code Project and thanks to all.

## History

- 4
^{th} August, 2010: Initial post