>> Sean: Why binary? Wouldn't it be much easier if they just used decimal numbers? >> DFB: Yes it would. This is a
fascinating story and it's one where what we've mentioned already - when you
and I started racing around Bletchley Park and talking about Tommy Flowers. He
is, if you like, right in the middle of this story.
Why binary why not decimal?
It's caused me to think about it. Because, if you think back to the pre-electronic
era, back to Victorian times, think of Charles Babbage and his famous
Difference Engines. They're, of course, just like the old-fashioned, mechanical,
hand-driven calculators - only a lot bigger. So the question was can you, on a
mechanical gear-wheel, grind ten teeth very accurately, and equal distances
apart, so you don't get slippage. You don't get 0 slipping into being 1,
Yeah? So it was a mechanical challenge. >> Sean: So 10 cog teeth doesn't sound like a
massive feat to deal with ? >> DFB: No it isn't - but they could do even more. What I'm trying to
say is: even earlier than that they could do more than that. There's been TV programs
on Greek Antikytheras that could predict solar eclipses. Absolutely finely
machined teeth, so yes
ten was pretty straightforward for Babbage and yet he still had complaints
from his gear cutters because the large-scale automation of manufacture
wasn't quite there in Babbage's time and he moaned like mad at the invoices, the
bills, he had to pay to his gear cutters. So that was the big problem in the
mechanical era. Things however did change enormously when we got - not just to the
electro-mechanical era, of relays, but when you say "I'm going to be purely
electronic". Then, back in those early days -
30s, 40s - you were talking about thermionic valves. Once again, that's vacuum
tubes for those of you in North America - who haven't watched the earlier videos!
What you have to say to yourself there, well, if I use those as a logic element,
on and off, you've got your cathode which boils off electrons, your anode with a big
voltage on it, sucking off the electrons up here, and in the middle
there's a grid. By putting what was called, I think, a 'bias voltage' on the grid. If you
put a heavy negative voltage on the grid it repelled the electrons back to the
cathode plate and didn't let them through. So you switched it off, So that was how it worked.
But you needed heaters to boil the electrons off the cathode. Heaters! Power! These things,
valves, are so power hungry it just isn't true. So on the one hand you are getting
this ability to do electronic logic elements, but the power consumption was a
problem all the time.
One reason to use binary, overwhelmingly, is it's perfect for the logic. But I think
the bigger question is when you start counting things - when you start doing the
arithmetic - does it still make sense to bust yourself to use decimal because
it's what we're used to?
Well "yes and no" I think, is the answer to that
The good thing about using decimal - let's say that first of all - is that you need fewer
digits, yeah? But binary's a lot longer than decimal. Obvious example, of course, is log to the
base 2 of 10 equals 3.322. And if anybody wants to produce a T-shirt with that on I might even
buy one. What it tells you is how much more circuitry and components do you need if
you go for a binary computer than if you go for a decimal one. >> Sean: That is just telling us
how many more digits we need? >> DFB: Exactly! how many bits would you need
to represent 99 in binary? >> Sean: Well I know that 8 bits is 256. >> DFB: Yes but that's too many ... >> Sean: So 7 bits is 128 >> DFB: Exactly!
>> Sean: So that would encompass 99 right? >> DFB: Right! So 99 requires seven bits. So how does
that relate to this magic 3.322? Answer: a two-digit decimal number, two, if you multiply
it by 3.322, you end up with 6.644. Numberphile stuff! You
round up. You take the 'ceiling' of that which is the smallest integer
directly above it. You times the number of decimal digits by 3.322 That gives you
the number of binary digits. But if in doubt, you have to round up because you
must have a whole number of bits. So, straight away you can see, therefore, that
the thing that electronics engineers loved about binary was that it's simpler
to build. Now, that is so important, but they also realized that you would need
3.3 times as much circuitry if you did binary. So, there
was some argument that said "Well, even though binary is right for the logic in a
computer, is there anything to be gained by still sticking to decimal for the
arithmetic bit - for counting numbers up - not just for doing logic operations?" >> Sean: So you
could have kind of two areas to consider? One is the actual storage of the
numbers and one is operation of the computer, >> DFB: That's right. And I think the
person who really, you know, one's respect for him goes up all the time,
Tommy Flowers of 'Colossus' fame was absolutely on top of this. He'd done
digital logic for early digital switching experiments in the nineteen
thirties. He knew all about this stuff. Two of his engineers who've written up in
Jack Copeland's book - Gil Hayward and Harry Fensom - said "Tommy was always explaining to us
every valve you can save is that much less power, that much less heat to worry
about. If we use bi-quin ... >> Sean: bi what?! >> DFB: bi-qui .... bi-quin we can save 100-odd valves". And bi-qui or
bi-quinary, base 5. Two things: five is magic for Tunny traffic because we're coping with five-hole
paper tape. That's one good thing about it. The other good thing about it is you
know from the valve circuits we design that if you're going to count in binary
you only need two voltages - you can keep them miles apart, that's easy. Five
below ground potential five above. A ten-volt
span. Nothing's going to make minus five look like plus five. But the more we try to pack
different levels in - and we have to pack in ten levels - you know what happens? These
voltages drift! You start getting the voltage representing a six drifting a bit and it looks
like a seven. But he said: "My studies show that if we just use 5 voltages we can keep
them stable enough that they don't get confused". So he came up with this idea of
bi-quinary - basically two things linked in pairs. The left-hand one did 0 to 4. The right-hand
one also did 0 to 4, but knowing that it was on the right-hand side actually
represented 5 - 9. He said we do that chaps we save ... I think it was a hundred and
something valves. And it's worth it, because you've got to reflect that the power
consumption of Colossus was 6 kilowatts. You didn't want to go higher than that.
>> Sean: I can't help but draw a comparison here to the data-centre video. It's funny that it's kind
of come full-circle in a way?
>> DFB: Absolutely! You no sooner overcome the problems and like Steve Furber's stuff - you
know, with the ARM chip being low power consumption? Great to do it, but then
people just want more of them anyway! You still need a data-centre; you still need
massive backup power supplies of your own and you need cheap electricity. You
could say that the great advantage of that is that when you're not in a
data-centre the low power demands,
and so on, make these things possible. There's no way I want that thing
replicated using thermionic valve technology - not even by Tommy
Flowers! I do not want third-degree burns in my shirt pocket
thank you very much!