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An introduction to counting in binary and how and why computers use binary numbers

paper and pens

1) Explain that at a very simple level, computers have a torch inside them and ask them what states a torch can be in (on or off). Then explain that computers don't just have one torch in them, they have the equivalent of millions of torches all turning on and off millions of times a second.

2) Show them a two digit number in base 10, and get them to identify the tens and units. Explain that computers aren't very clever, they can't count to 10, they can only use 1s and 0s. 1 when the torch is on, and 0 when the torch is off. Get them to draw a 1 and a 0 on bits of paper and hold them up when you shout 1 or 0.

3) Draw a grid with 8, 4, 2, 1 across the top (in that order) and explain you're going to teach them to count the way that computers count. Gradually fill in the grid as below, get them to copy the grid as you draw it. Fill in the first two rows, and then get them to guess how a computer counts to 3 using only 1's and 0's (ons and offs). Tell them that it's the same as tens and units, but the computer uses 2s and 1s.

8,4,2,1

0,0,0,1 = 1

0,0,1,0 = 2

0,0,1,1 = 3

0,1,0,0 = 4

0,1,0,1 = 5

They should be able to start guessing the right answer from 3 onwards.

4) Explain that to do all the stuff computers do, they don't just have 'torches' in them they have special boxes, called 'gates' that look at all the torches and check if they're on or off. Different types of gates do different things.

5) Play a game with a NOT gate. Explain that the box with this gate in does the opposite of the torch it's looking at it. Play holding up 1 or 0 and they have to hold up the opposite - 0 or 1.

6) Play a game with an XOR gate (call it an OR gate for short. This gate, when you show it two torches can tell if each torch is on or off. If both are off it shows a 0, If both are on it shows a 0, if 1 OR the other is on it shows a 1.

7) If they haven't fainted, show them how a computer does basic addition using an XOR gate and an AND gate. Get one beaver to be the XOR gate, and one to be the AND gate.

0+0 gives XOR 0 + AND 0 = 0

0+1 gives XOR 1 + AND 0 = 1

1+0 gives XOR 1 + AND 0 = 1

1+1 gives XOR 1 + AND 1 = 2

We only got as far as step 6, but at least half the group got how to count in binary and understood the idea of 'logic gates'. And had fun drawing 1s and 0s.

- binary
- coding
- computers
- logic

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