There are only 10 different sorts of people in the world

[Bert]

Those who understand binary notation and those who don't.

[sophieb]

I'm one of the ones who don't! If anyone could tell me in really terms that would be great!

[sophieb]

Sorry I meant really simple terms!

[vehelpfulguy]

I will try and explain.

Humans tend to count in tens (cos of our fingers and thumbs I suppose). Decimal notation.

When we get up to 9 we start again in that column with 0 and move a 1 into the tens column so it becomes 10.

Same with 99, next is 100 and 999, next is 1000 and so on.

Lets suppose we did not have 10 fingers and toes and just one limb. So the only numbers in our counting system were 0 and 1. There are no other numbers just 0 and 1.

This is called binary and all the computers in the world work on the binary system. Also all digital devices like CDs, DVDs, digital phones, digital TVs, digital cameras etc

ALL information is held as a ZERO or a ONE.

So we start counting with ZERO (0). Next number is ONE (1).

We have no 2, so the next number is 10 (not ten but 1 and 0).

So in Binary 10 is actually 2 hence the joke.

To continue the counting, after 10 we have 11, but we cannot go to 12 so must go to 100, then 101, then 110, then 111 then 1000 nd so on.

So in binary 1000 is actually 8.

This may sound confusing but is very important in the world of computers where information is important, it is much easier for a computer to count in just 0 and 1 than have thousands of numbers.

[vehelpfulguy]

Lets try and give an example.

Most light switches are simple ON or OFF. There is nothing in between, the light is either on or off.

In binary terms this could be 0 for off and 1 for on.

Now suppose you have a dimmer switch. It rotates round from fully off to fully on. Lets call fully off 0 and fully on 10.

Suppose I asked you to set it at say 4.

This would be very difficult. You may get it NEAR 4, but not exactly on it. And in the world of computers and digital devices NEAR is not good enough.

So lets replace the dimmer with 4 normal light switches, which just offer ON and OFF.

When all four are OFF you can think of that as 0000. This is like the dimmer fully OFF.

When all four are ON your can think of it as 1111. This is like the dimmer fuly ON.

If you turn on just the last switch, and so now it is 0001. This is setting 1 on our dimmer scale.

Turn ON the third and OFF the fourth, so it is now 0010.
This is setting 2 on our dimmer scale.

Turn on the third AND fourth, so it is now 0011. This is setting 3 on our dimmer scale (2 + 1)

Turn ON the second and OFF the third and fourth, so it is 0100.

This is setting 4 on our dimmer scale.

So with 4 "binary" light switches we can get exactly 4, which we could not do with our dimmer switch.

This is why all computers and other digital devices use binary, it is much more accurate.

In fact every CD and DVD you own has all the information stored as 0 and 1.

[sophieb]

Thank you so much! I get it now from the light switch explanation! I could never get the hang of it at school! My maths teacher was pretty sexist and didn't bother with in-depth explanations for girls!

[sophieb]

*** for you vehelpfulguy since i can't rate your answer!

[greenrook]

Cheers vehelpful, I just read your explanation for sophieb and I'm going to have a lie down, see if it helps this headache just came on...!

[vehelpfulguy]

Have a look at the Windows calculator, that can count in binary.

Open the calculator, and select View then Scientific. It gets bigger.

There are 4 buttons (Hex, Dec, Oct, Bin). Select the Bin (Binary) button.

The only two numbers available are 0 and 1.

Select + (plus) then 1 then = (equals).

The output shows one.

Add another one, the output shows 10.

Keep adding 1 and watch the binary numbers go up.

(by the way the Hex option is using a base 16 not 10. This is also used in computers).

You have the numbers 0 to 9, then ABCDEF representing 10 to 15. We will leave that for another day.

[Bert]

I'm so pleased I really started something! Most of the "questions" on this part of Answerbank get no response at all, or, at best, a few jokes in the same vein.

What I like about this joke is that it can only really work when it is written down and read. You cannot tell this joke verbally.

[Jovica]

Wow, what's your day job vehelpfulguy?

[heathfield]

Er, with the 4 light-switches on, we would get 15 on the dimmer scale, not 4.

[Bert]

Heathfield,
vehelpful wasn't saying that the four light switches were on for setting number 4. The setting number 4 is 0100. The trouble with the dimmer analogy is that, if we are imagining 4 lights of equal brightness, then settings 1000, 0100, 0010 and 0001 are all the same (i.e. only one light is on), and 1111 is only four times as bright as any of them.

[vehelpfulguy]

I realise the dimmer analogy does stand too much scrutiny, but I was trying to think of a simple way of expalining binary.

I seems an easy thing to explain, but you try and write it down in simple terms, it is not that easy.

[Bert]

No criticism of your explanation intended, vehelpful. I certainly appreciate that it is difficult to explain, and I was just trying to say, for heathfield's benefit, that analogies should not be pushed too far. Heathfield seemed to be confusing the fourth setting with having all the switches on. Maybe we could use the dimmer analogy if each light was twice as bright as the one before (i.e. the one operated by the 'switch' to the right). The dimmer scale would need to run from 0 to 15, rather than 0 to 10. Then setting number 4 (0100) would be 4 times as bright as setting number 1 (0001).