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?
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
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
- 20 = 1
- 21 = 2
- 22 = 4
- 23 = 8
- 24 = 16
- 25 = 32
- 26 = 64
- 27 = 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?