The Last Theorem - Arthur Charles Clarke [52]
That turned out to be a tall order. Two of the ten-year-olds never stopped crying, and several of the others could not seem to take their eyes off the rifle-carrying pirate who patrolled the deck. It may have been that Ranjit made it even harder on himself, because rather than doing the simple and never-failing Russian multiplication thing again, he decided to show the children how to count on their fingers, binary style.
It was not a success. Clearly none of the passenger children had ever heard of binary numbers before. When Ranjit informed them that if you wanted to say you had one of something in binary, you could just write the old familiar one, but if you had two, you had to write it as one-zero, and three as one-one, the incomprehension was palpable.
He pressed on gamely. “Now we come to the counting-on-your-fingers part,” he told them, holding up his two hands. “What you have to do now is assume that every one of your fingers represents a numeral—and, yes, Tiffany, I know what you’re going to ask. Yes, we do count the thumb as a finger.” (Tiffany hadn’t said anything, but cheerfully nodded.) “Each numeral has to be a one or a zero because that’s all you have to work with in binary arithmetic. When the fingers are retracted”—he made two fists—“each finger is a zero. So now look here.” He laid his two fists on the table-top before him. “In binary these ten retracted fingers represent the number zero zero zero zero zero zero zero zero zero zero. Which is just another way of saying that zero is the number all ten of the zeros represent, because no matter how many zeros you write down, it’s still just zero. But now look at this.”
He stuck out all the fingers on both hands. “Now they’re all ones, and the binary number I’m displaying is one one one one one one one one one one. And that means, if you want to express it in the decimal equivalent, that you’re writing a one for the last numeral one in the line, plus a two for the numeral one next to it. Plus a four for the one next to that—doubling each time, you see, all the way up to five hundred and twelve for the last numeral one at the end of the left hand. And so you have written—”
He did the arithmetic with a crayon on a scrap of paper:
“And if you add them all up together you get—”
“And so you’ve counted on your fingers all the way up to one thousand and twenty-three!”
Ranjit paused to look around at his audience. What he got back was not what he had hoped for. The number of weepers had risen to four or five, and the expressions on the other faces ranged from simple confusion to resentful bafflement.
Then, tardily, questions did begin.
“Do you mean—”
“Wait a minute, Ranjit, are you trying to say—”
And finally, rewardingly, “Oh, let’s see if I got it right. Let’s say we’re counting fish. So what that numeral one at the right-hand edge means is that there’s one pile of fish that has only one fish in it, and the numeral one next to it means there’s another pile that has two fish, and piles with four fish and eight fish, all the way up to the pile—that’s the numeral one at the other end—that has five hundred and twelve fish in it. And you add all the piles together, and altogether you’ve got one thousand and twenty-three fish. Is that it?”
“It is,” Ranjit said, gratified in spite of himself. Gratified despite the fact that the only children who had responded at all were Dot and Kirthis Kanakaratnam’s kids, and the one who had really understood was, of course, Tiffany.
Kanakaratnam himself didn’t seem to worry about Ranjit’s poor reception. When he joined Ranjit for lunch—two kinds of soup, three different salads, and at least half a dozen entrées on the menu—he said approvingly, “You did yourself some good today.” He did not say in