OT -binary arithemtic?

[David WE Roberts]

Just watched a Jools Holland retrospective on iPlayer.

He was celebrating 250 programmes - so there was a chess board on which there was one videotape on the first square, two on the second.....

Only the truly computer literate (and vaguely uncontrolled) were shouting at the screen "It's 256 shows you stupid f***kwit!!"

Oh, does nobody count in binary anymore?

[and my 500Gb drive is really only 465.2Gb because they use K for '1000' instead of '1024' - bl**dy marketing.]

Where is hexadecimal when you need it?

Grumble....

[Bill]

In message , David WE Roberts writes

There are 10 types of people in this world, those who do and those that don't.

[Ronald Raygun]

That reminds me of the story of the king who was marrying off his daughter to a prince of the kingdom next door. As folk in that part of the world were keen on chess, and it was a rice-based economy, the king thought he would include in the dowry a token quantity of rice, to be presented on a chess board.

One grain on the first square, two on the second, four on the third, and so on, doubling each time. He got his court mathematician in to work out how big to tell his carpenter to make the board.

Naturally the mathematician had to persuade the king to drop the idea.

[Roger Mills]

Turn it on its head, and you get the binary method of sharing . . . If you want to divide (say) a cake among a number of people, the first person gets a half, the next person gets half of what's left and so on. That way, you never run out - provided you're good at splitting crumbs!

[Clive George]

They had a similar problem in Norman Hunter's Incrediblania.

[Matty F]

A chessboard having 64 squares - So was there one more tape on the next square, i.e. 1,2,3,4, making 64 tapes on the last square, a grand total of 2080 tapes?

Or did the number of tapes double on the next square, i.e. 1,2,4,8, making 9223372036854780000 on the last square, a grand total of 18446744073709600000 tapes? How long are these programmes?

[John Rumm]

Or the riddle of how to cut a round cake into 8 equal portions with only

3 straight cuts...

[dennis]

I can think of two ways.. One works with layer cakes the other requires moving the bits.

[David WE Roberts]

The first row (8 squares) of the chess board had been filled with the usual binary progression:

1,2,4,8,16,32,64,128 The first square of the second row (next to the 64 square) had the pile of 250 tapes. So, 6 short of the full number of 256. I don't think that they have any hope of completing even the second row of the board :-)

[David WE Roberts]

Horizontal cut then two vertical cuts at right angles? Wouldn't really give consumer satisfaction with a Victoria sponge though.

[Ronald Raygun]

That doesn't entirely make sense.

For one thing, the first square of the second row would be next to the

1 square (if scanning) or the 128 square (if snaking), not the 64 square.

For the other, unless the first row of tapes were nothing to do with the man himself, there'd be no need to begin a second row at all, and the

8th square (which *is* next to the 64 square) should have only 123 tapes on it, thus adding up, with the 127 tapes on the first 7 squares, to the required 250.

[David WE Roberts]

My bad - it was next to the 128 square. [Mr. Picky decided not to wriggle around the fact that it was diagonally adjacent to the 64 square - got me bang to rights guvnor.]

As you say, if they filled the first row to generate 0xFF tapes they should have had 255 tapes. Neverthless IIRC they had turned the corner for the biggest stack. I assumed that they were doing the traditional 'chessboard thing' with a binary progression else why the massive chess board with increasing numbers on each square? I'll probably have to go back and watch it again on iPlayer just to see how inaccurate my recollection is. Probably as bad as my binary arithmetic :-(

[Probably also difficult or impossible to pile 128 videotapes (Why videotapes? Does the BBC still record to digital tape?) on the 8th square.]

[Ronald Raygun]

It's not difficult if you make the squares big enough and pile the tapes more sensibly than as a single stack.

If instead of progressing binarily they had progressed linearly, piling just one more tape on each square than on its predecessor, they would have needed 23 squares and the tallest pile would have needed only 22 tapes.

The 23rd square would then have been nearer to the 64 square than to the 128 square, except that they would not have been called 64 and 128 but 7 and 8. :-)

[John Rumm]

That's the one - each cut must bisect all the pieces so you get a doubling each time, and you need a cut on each axis. No need to move bits between cuts. The Victoria sponge problem (aka the iced cake problem) is however present.

[geoff]

In message , David WE Roberts writes

And a 2TB HD is only 1700gig

calm down dear its only a counting system

[Andy Burns]

Once you get into the range of terabytes, pretending the difference between decimal powers and binary powers doesn't matter gets very silly, you have to start using Gibibytes and Tebibytes instead of Gigabytes and Terabytes.