Peasant or binary multiplication

In base 2, long multiplication reduces to a nearly trivial operation. For each '1' bit in the multiplier, shift the multiplicand an appropriate amount and then sum the shifted values. Depending on computer processor architecture and choice of multiplier, it may be faster to code this algorithm using hardware bit shifts and adds rather than depend on multiplication instructions, when the multiplier is fixed and the number of adds required is small.

This algorithm is also known as Peasant multiplication, because it has been widely used among those who are unschooled and thus have not memorized the multiplication tables required by long multiplication. The algorithm was also in use in ancient Egypt.

On paper, write down in one column the numbers you get when you repeatedly halve the multiplier, ignoring the remainder; in a column beside it repeatedly double the multiplicand. Cross out each row in which the last digit of the first number is even, and add the remaining numbers in the second column to obtain the product.

The main advantages of this method are that it can be taught quickly, no memorization is required, and it can be performed using tokens such as poker chips if paper and pencil are not available. It does however take more steps than long multiplication so it can be unwieldy when large numbers are involved.

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

11 3
5 6
2 12
1 24
---
33
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 distributive, so:

Dyma graff sy'n dangos yr arbediad nwy a gefais trwy newid fy hen fwyler nwy am un newydd.

O ystyried cyfartaledd y defnydd nwy yn y 3 blynedd cyn newid y bwyler (750 uned y flwyddyn), dyma'r defnydd nwy fel canran o 750 uned:

2005-2006 = 793 uned - 106%
2006-2007 = 688 uned - 92%
2007-2008 = 769 uned - 103%
2008-2009 = 429 uned - 57%
2009-2010 = 374 uned - 50% [TARGED GAEAF YMA]

Mesurau arbed egni i leihau'r nwy a ddefnyddir

1. Heb ddefnyddio gwres canolog buaswn yn defnyddio < 100 uned y flwyddyn. Felly mae tua 300 uned yn cael ei ddefnyddio i gynhesu'r ty yn y gaeaf. Yn ol yr ystadegau ar wefan yr EST (Energy Saving Trust) mae tua 30% o'r gwres a gollir o'r ty yn mynd trwy'r waliau, felly os y gallaf hanneru'r golled hon buaswn yn medru arbed [(329/3)/2] = 55 uned. Felly buasai'r defnydd blynyddol o nwy yn gostwng (429 - 55 = 374) = 50% o'r cyfartaledd cyn y system gwres canolog newydd.
2. Symud yr ystafell fyw o'r ystafell fwyaf i'r ystafell biano. Mae llawer o wres yn diflannu i fyny'r simdde ac allan o'r tai haul o bobtu i'r ystafell fawr. Felly, trwy symud y teledu i'r ystafell biano ni fydd angen cynhesu'r ystafell oer hon.
3. Mae angen gosod falfiau thermostat ar rai o wresogyddion y llawr isa.
4. Mae angen insiwleiddio'r fynedfa i'r to.
5. Rhaid lleihau'r drafftiau o amgylch y ffenestri.

Dyma ddau ddarn punt ffug a dderbyniais yn newid ym mhwll nofio Woolston - 24ain o Dachwedd 2008.




Ochr pres - darnau punt Cymraeg ydynt - ond dim ond ar un mae'r geiriau "Pleidiol wyf i'm gwlad".