Page:Astounding Science Fiction (1950-01).djvu/112

BRASS TACKS

Perfectly correct! Now—wonder what ancient, nameless genius, not knowing the binary system, figured it out?

Dear Mr. Campbell:

I especially enjoyed your simple system of multiplication in the June issue. The only thing that ruined it was that "Why?" stuck on the end. It forced me to stay up half the night trying to figure the darn thing out. Finally out of sheer exhaustion, I came up with a fairly logical solution.

Here it is: the multiplication system is based on the binary system of numeration. (The numerical system using only two digits, 1 = 1 2 = 10 3 = 11 4 = 100 etc. See pp 94-95 May 1949 issue of ASF.)

Take a simple multiplication like 9 X 6 for instance. Now, set the problem up in the two columns and proceed according to directions, dividing the smaller by two and multiplying the larger by two the same number of times. The division of the smaller number really converts it to the binary system. The odd number = 1; the even = 0(1). Then converting the other column to the binary system, you have a form of binary multiplication. (2)

(1)	${\begin{matrix}6&\ &0\\3&=&1\\1&\ &1\end{matrix}}$$\qquad 6=110$$\qquad 9=1001$

(2)	${\begin{array}{lrr}&&&&1001\\&&&&{\mbox{X}}110\\0\,{\mbox{X}}&1001&&=&000000&=&0\\1\,{\mbox{X}}&1001&{\mbox{X}}\,10(2)&=&1001{\scriptstyle (0)}&=&18\\1\,{\mbox{X}}&10010&{\mbox{X}}\,10(2)&=&1001{\scriptstyle (00)}&=&36\\&&&&110110&=&54\\{\mbox{a}}&{\mbox{b}}&&&{\mbox{c}}\end{array}}$