Editing Multiplication algorithm (section)

====Examples====
This example uses peasant multiplication to multiply 11 by 3 to arrive at a result of 33.

 Decimal:     Binary:
 11   3       1011  11
 5    6       101  110
 2   <s>12</s>       10  <s>1100</s>
 1   24       1  11000
     ——         ——————
     33         100001

Describing the steps explicitly:

* 11 and 3 are written at the top
* 11 is halved (5.5) and 3 is doubled (6).  The fractional portion is discarded (5.5 becomes 5).
* 5 is halved (2.5) and 6 is doubled (12).  The fractional portion is discarded (2.5 becomes 2).  The figure in the left column (2) is '''even''', so the figure in the right column (12) is discarded.
* 2 is halved (1) and 12 is doubled (24).
* All not-scratched-out values are summed: 3 + 6 + 24 = 33.

The method works because multiplication is [[distributivity|distributive]], so:

: <math>
\begin{align}
3 \times 11 & = 3 \times (1\times 2^0 + 1\times 2^1 + 0\times 2^2 + 1\times 2^3) \\
& = 3 \times (1 + 2 + 8) \\
& = 3 + 6 + 24 \\
& = 33.
\end{align}
</math>

A more complicated example, using the figures from the earlier examples (23,958,233 and 5,830):

 Decimal:             Binary:
 5830  <s>23958233</s>       1011011000110  <s>1011011011001001011011001</s>
 2915  47916466       101101100011  10110110110010010110110010
 1457  95832932       10110110001  101101101100100101101100100
 728  <s>191665864</s>       1011011000  <s>1011011011001001011011001000</s>
 364  <s>383331728</s>       101101100  <s>10110110110010010110110010000</s>
 182  <s>766663456</s>       10110110  <s>101101101100100101101100100000</s>
 91  1533326912       1011011  1011011011001001011011001000000
 45  3066653824       101101  10110110110010010110110010000000
 22  <s>6133307648</s>       10110  <s>101101101100100101101100100000000</s>
 11 12266615296       1011  1011011011001001011011001000000000
 5  24533230592       101  10110110110010010110110010000000000
 2  <s>49066461184</s>       10  <s>101101101100100101101100100000000000</s>
 1  98132922368       1  <u>1011011011001001011011001000000000000</u>
   ————————————          1022143253354344244353353243222210110 (before carry)
   139676498390         10000010000101010111100011100111010110