MULTIPLICATION WITH A DIFFERENCE B

are taken. The first term in the right column will always be
taken when the multiplier in the left column is odd. But the
first term in the left column is always the multiplier itself, so
that when the multiplier is odd, the first term in the left
column is odd. So much is clear. What is not so clear is why
the subsequent terms which must be taken in the right
column are always on the same lines as odd numbers in the
left column. The last term is always included for the last
term in the left column is always 1 and therefore odd. The
remaining problem is how the intervening included terms
‘know’ they have to be odd.

The general theory may be explained thus: Take any
figure (say 99) and split it into powers of 2 (99 =64 432 +2
+1=28+42542-1). Now instead of writing g9 in the left
column, write the factors there and watch what happens:
when we divide successively by 2.

Left Right
Column Column Term
26
2 5
99 = B 2 Ist

2% 4 2nd

i

24:{23 8 grd
{
{

12~ 2: 16 4th
22

D 7= 5 32 5th

3={f 64 6th

1= 8 128 7th

In the left column the plus-signs are omitted between the

 

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