How would you explain binary to your grandmother?

Answer 1

"Count to twenty like you normally would. See what happens at 11? Ok, now do the same thing, but leave out 2 to 9."

Answer 2

"Imagine you had only 2 fingers...."

Answer 3

"Oh grammy, it's just one of those silly t-shirts we programmers like to wear."

She wouldn't be interested in the actual answer anyway. This concept (a question best left answered inaccurately) might be hard to accept for a geeky type, but it's true.

Answer 4

Explain how 'unary' - a number system using only a single symbol - would work. Binary's then only twice as complicated as that ;)

Answer 5

Tell her that binary is how computer's count, because they are made of switches which can either be on (1) or off (0). Show her this: http://www.instructables.com/id/Binary-Counting/

Answer 6

When I learned arithmetic at school we would break numbers like 3145 into

Thousands:3 Hundreds:1 Tens:4 Units:5

in order to learn about place value. I would explain to granny that computers are not as clever as us (something she would happily agree with) and so they can only use two digits - 1 and 0. This means that they have to use a different place value scheme. Instead of Thousands, Hundreds, Tens and Units they have to use eights, fours, twos and units. So 1001 would be

Eights:1 Fours: 0 Twos:0 Units:1

Which comes out as 9 in decimal.

Answer 7

Start with decimal and remind her about how it works. Establish that there are ten digits, ten possible values for every place. When you count up to 9 in the ones place and you run out of digits, to write the next number, you increment the tens place and wrap the ones place back to zero. Just to establish that, count: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. Make a point that "ten" is an amount, but "one zero" is how you write it because that's decimal. And the amount "eleven" is written "one one". The reason is because in decimal you have ones, tens, and hundreds. Powers of ten. So with one ten and one one, you write "11".

Then try base 5. Count in it: 0, 1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21 ... And whatever you do, when you get to that "10", don't say "five", say "one zero". Impress upon her that this is because in base 5 you don't have a tens place, you have a fives place. You have one five and zero ones, so that's "one zero" – "10". Make the point that, even though it is the amount "five", it's the way you write it that makes it base 5 or base 10.

Now give binary a shot. Call it "base 2" so it makes more sense. 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001... Explain that now the places are powers of two just like decimal has powers of ten. So, you have ones, twos, fours, eights and so on. As you count up, give special emphasis to how the rollovers work and note that they happen a lot more often because there are few digits.

If she still doesn't get it, try base 5, 4, 3, and then 2 again.

Answer 8

Grandma, remember morse code and telegrams? It's like that. The tiny little people inside the computer have morse code tapper thingies, and that's how they talk to each other.

Answer 9

Go to the kitchen, or another room with two lights.

Explain that the lights are either on, or off - each light can only count up to 1.

By combining lights, though, you have many combinations of on and off, and with two lights you can count up to 3.

Then you can go into how it relates to base 10 if you think they're interested, but usually by this time they've wandered back into the tv room.

Answer 10

"An office has 3 light switches by the door. They control the lights in order: near the white board, over the door, and the back of the room. We can summarize the way the room is lit by saying the state of the lights in sequence, 'on-off-on' or more tersely, 101."

Answer 11

I think you should not explain the way binary works at all, since this is only secondary to understand that T-Shirt. Just tell her / them that binary is another way to count* and that 10 in binary is the same as 2 for ordinary people. That's all one has to know to get the joke.

*The fact that computers use binary is not key to understanding the joke, but I would actually mention it so that your audience knows that binary has a practical meaning, e.g. was not invented to make this T-Shirt possible...

Most people will be satisfied (or even annoyed) by then. Should somebody really ask for the details, check back for the other answers given before.