**Warning! Obligatory number system description ahead.**

While we convert numbers based on a decimal system, computers use a binary system, understanding ons and offs as numbers.

Decimal (base ten): If you add one to nine, you have to carry, and you get ten.

Binary (base two): If you add one to one in binary, you have to carry, and you get ten.

Binary conversion works with liquid measurement: one cup + one cup = one pint; one pint + one pint = one quart; one quart + one quart = one half gallon. Think of one cup as 1, two cups (a pint) as 10, three cups (a pint and a cup) as 11, four cups (one quart) as 100, and so on.

Easy enough. What if you had a byte of information to convert, though, something that looked like this?

10101010**Obligatory number system description off.**

It's time to bring out the Post-its and Popsicle sticks.

## Step 1: Tools and Materials

A pad of notes

8 sticks

Glue or glue stick

Highlighter (or any marker that doesn't bleed through the notes)

## Step 2: Make Your Ones and Zeros Flip

Take a stack of two notes. On the top write a zero, then fold it in half and write a one.

I liked constructing it this way because it reminded me of those old digital flip clocks.

## Step 3: Line Up Your Binary Numbers

Make a column of eight ones and zeros.

## Step 4: Line Up Your Decimal Numbers

- 2
^{0 }= 1 - 2
^{1 }= 2 - 2
^{2 }= 4 - 2
^{3 }= 8 - 2
^{4 }= 16 - 2
^{5 }= 32 - 2
^{6 }= 64 - 2
^{7 }= 128

## Step 5: Make 'em Flip

Glue and apply sticks to the bottom of the notes when set to "0".

## Step 6: Start Converting

Set your binary number. Move the stick to the bottom for "0", or low, and to the top for "1", or high (If you were a computer, you'd be feeling some voltage).

Add all the decimal numbers on the right. You can use a note on the bottom to do your sums.

So what about that number: 10101010?

That's 128 + 32 + 8 + 2.

Binary 10101010 = decimal 170.

Have fun flipping.

## Step 7: Variations, Improvisations, and Meditations

How about a hinged wooden version that goes clackety-clack, or a flipping byte converter run by a micro-controller?

Coffee stirrers actually work much better than Popsicle sticks. As you can see, I wrote a note at the top. What kind of notes would you write? Would you put a white board or black board at the bottom? How would the flipping converter work four bits at a time? What would an octal or hexadecimal converter look like?

## Discussions

5 years ago on Introduction

Wow - that's pretty great.