I’ve seen that two other people have already written about this book (one being my applications partner, which makes this post clearly very late but I wanted to finish the book), and though they’ve written wonderful things about the subject, I wanted to update what they’ve said with a concept that I took from the book, which, I feel, is the magic behind computers. That concept is Bits (which either in life or in ICM or PCOMP or in this book, we’ve understood as a binary digit). What is a Binary Digit? What is a digit? Why do we choose ten rather than 8, rather than 32 or 95?
In the beginning of the book, he talks about communication. How, in certain communication, the best understanding we can share are two values, on or off. Morse Code and Braille both use these concepts over and over. Putting an on and an off in sequence with other on’s and off’s create a code that can manipulate information in a way that can be understandable. But is on and off the only way that we can learn? No. What about changing the length of on or off? That will give us different values like Hannah talks about with morse code and logic. How can you manipulate on and off to give you different things as Henry says about electronics. I don’t think you can truly know withough as Henry says, “Knowing what you’re working with.” That is why understanding the bit and what the computer does with it is the most important issue of not only being able to artistically manipulate a computer but also being able to communicate with computers. The bit is the lowest value of information, on or off. This is the infrastructure of computers.
Charles Putzold begins the discussion of bits talking about base ten, our number system. He says that we clearly count in base ten because of how many fingers we have. He said that one of the most significant mathematical discovery came with the discovery of zero. That made it possible to think about the nothing integer or the reset digit. The interesting part comes when we are counting up and we run out of fingers, at 9. What did we figure out? to reuse the digits and make 10. which is just starting the counting over but holding a remainder to remember that we’ve already been through the digits once. This is super important because as we’ll see this is the way to count in other more complicated number sequences.
Next he talks about what if we weren’t humans but rather what if we were cartoon characters. We’d only have 8 fingers and toes. Then we wouldn’t have a use or a reason to count to 8 or 9. We’d count to 7 and then 8 would turn into 10. Think about it. 8 would be the reset. 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20 etc. It doesn’t stop there. What if we were all crabs. Then our hands would be claws and we’d count in base 4. 1, 2, 3, 10, 11, 12, 13, 20 and so on. And it would be the same if we were dolphins. Dolphins have two flippers and therefore would count in base two, binary, ones and zeros. 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111. That is the first 16 numbers in binary. It’s very simple. You count 1. Then instead of 2 it would be 10 because you reset the count since there’s only a 1 and a 0 in your world. Don’t understand. Think back to when were counting base 8. We had no use for the number 8 just like when we count in base 10 we have no digit higher than 9. We get to the last digit and start over storing a remainder. That’s all base ten is. It just constantly stores remainders as you count up. look at the sequence of binary numbers counting up to 16 base ten. notice how everytime it reaches what would be two in our base ten. It moves over a number storing the reset. 1, 10 (stored), 11, 100(stored), 101, 110(stored), 111, 1000(stored). This is how a computer works. It’s constantly storing all of the counts and manipulating them to give different values. That’s also how electricity works. It’s on or it’s off, 1 or 0. And chips that have switches (on or off) store this like memory. It’s a little more complicated the way chips are made to store electrical impulses and quite beyond the topic but I really wanted to uncover the magic of counting in base two as Charles Putzold did for me. I hope you enjoyed it as much as I did. Let me know if I didn’t make sense.