Adventures of My Pet Bit: Can bits count in another way?

(Note: For the activity maybe a hexadecimal colour by number using ‘Short Hex’?)

Whew, writing out binary is sure hard work and it is confusing for us humans to read too. Lucky for us, there is a faster and easier way to write out binary using something called Hexadecimal Code. If you remember, normally we count in what’s called decimal or base-10.  Hexadecimal is the name that we have given to base-16.

Hex codes are used in many areas of computing to simplify binary codes. It is important to note that computers do not use hexadecimal – it is used by humans to shorten binary to a more easily understandable form. Hexadecimal is translated into binary for computer use. [Link] The main reason why we use hexadecimal numbers is because it is much easier to express binary number representations in hex than it is in any other base number system.

It looks like we have a problem. We might be able to count on our fingers in base-2 (binary) or base-10 (decimal) but we don’t have sixteen fingers so how can we count to base-16 when we don’t have enough digits or fingers to count on?

Lucky for us, mathematicians figured out that we can can use  0 through 9 like we are used to in base-ten but because we still need six more digits we will also add A, B, C, D, E, and F.

That can be a little confusing, because now when we write numbers in hexadecimal, they can actually have LETTERS in them! But you get used to it after awhile and it is going to be way faster for us to write bigger numbers.

Hex can be used to represent colours on web pages and image-editing programs using the format #RRGGBB (RR = reds, GG = greens, BB = blues). The # symbol indicates that the number has been written in hex format.

Adventures of My Pet Bit: Can bits count?

It is easy for bits to count to ten, they just do it differently from the way you and I do.  I am sure you know many different ways to count to ten.

What’s that? You only know of one way to count to ten? Really?!? But, are so many wonderful and different ways to do it. It seems a shame to only be able to count to ten in one way so let me explain how your pet bit does it.

This is the way you and I were taught to count to 10 on our fingers.
[Image Credit]

We tend to think it’s perfectly natural to count this way since we grew up counting on our fingers but unlike us, bits don’t have fingers! I know it is hard to believe but there are many ways to count besides the one we are used to.

The system of number we use every day is called the decimal system. Our number system contains numerals (or digits) only from 0 through 9. Since there are 10 numbers, mathematicians decided to call this system of numbers ‘base-10’.

The system of numbers that bits use is called the binary number system. Unlike our system of counting it only has two numbers: 0 and 1. Because there is only two numbers, mathematicians decided to call this system of numbers ‘base-2’.

Now that we understand the concept of a ‘number base’ the basics of counting in binary should be a little easier. The important thing to remember about working with number bases is that they are just different ways of writing down numbers.

 

Unlike you and me, bits can actually count to ten without having to write down any numbers at all. How amazing is that?  When bits get together in a group to count in binary they use two different colors. A group of bits use black to represent the number 0 and they use red to represent the number 1.  This still works though even though they are using a system of two colors instead of two numbers.

The good news is that even though you can’t change colors like a bit does, you can still use your fingers to do the same style of counting. And unlike your pet bit you won’t even need to find a bunch of friends to get together to be able to do it. How lucky is that!?!

Finger Binary is a system for counting binary numbers using only your fingers. In Finger Binary, it is actually possible to count  all the way to 1023 using both of your hands instead of only to 10.

[Image Credit] [Image Credit]

Now here is where it starts to get tricky so pay close attention. Remember that you just learned that when bits get together in a group to count they are using two different colors, black (representing the number 0) and red (representing the number 1). A raised finger will represent a red bit ( or a 1), and a lowered finger represents a black bit ( or a 0). I know this all sounds super confusing but don’t you worry!  For today, we are just going to learn to count to 10 on one hand. When I first learned how to count like a bit I got really frustrated because I found it really hard and overwhelming at first so we will keep it super easy to start out with.

Counting in binary is not an easy skill to master so don’t get mad at yourself if you find it hard too understand at first. If you just keep practicing counting this way over and over again, I promise you’ll get it. It is fun and exciting to be able to know be able to count to 10 while only using one hand. While all your friends will only know how to count to five on one hand you will know a secret way that your pet bit taught you so you can count all the way to 10 just using one hand instead.

Counting in binary is similar to counting in any other number system. When the symbols representing successively higher values are exhausted, the next-higher digit is incremented, and counting begins at 0. In decimal, counting proceeds like so:

00, 01, 02, … 07, 08, 09, 10, 11, 12, … 17, 18, 19, 20…

When the rightmost digit reaches 9, counting returns to 0, and the second digit is incremented. In binary, counting is quite similar, with the exception that only the two digits 0 and 1 are used. When 1 is reached, counting begins at 0 again, with the digit to the left being incremented: 000, 001, 010, 011, 100, 101, 110, 111…

 

[Image Credit]