The logic behind Ethiopian multiplication.

This method of multiplication is also called Egyptian Multiplication (as believed it was developed in Egypt).

How it Works.

• write two no in the adjacent columns(smaller one in left side,


• In the left column recursively halve the number, discarding remainders,
  


• In the right column recursively double the number and write the result below, do this unlit left column shows 1,
  


• Test for the left column if it is odd then add corresponding no in the right column.
  
  

Example

A = 34;
B = 12;

B	A
12	34
6	68
3	136
1	272

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408
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12*34 = 136+272
= 34*4 + 34*8
= 34(4+8)
= 34(2²+2³)
= 34(12)

The main idea is that break the first no in the power of two and multiplication with 2 is easier. Then add to obtain result.