January 31st – Binary

Like one of my students – I’m turning everything in at the last moment!  Whew – finally caught up, the next challenge is to get ahead…

As I’ve been quickly rushing through a lot of these final post, I’ve been trying to link them together and every once in a while they are random, this is one of the latter.  When I saw 31, I immediately thought of Binary Code or base 2.  Base 2 is one of my favorite subjects to teach because it really feels like you’ve accomplished something when you’ve “cracked the code” and are able to read numbers in binary – and often times the skill transfers to Octal and Hexadecimal number systems as well!

January 31st – Binary Code or Base 2

We live in a Base 10 world so it’s difficult for a lot of people to not see “10” as ten, but breaking it down into one “block” of 10 and zero “ones” is the mind shift that needs to happen.  As that abstraction happens and student are able to recognize the symbolic meaning of things rather than the meaning that they attached to it so long ago.  10 in binary is actually “2” because you have one “block” of 2 and zero “ones”.

Decimal has the prefix “deci-” meaning ten, binary has the prefix “bi-” meaning two.  Decimal is powers of ten, starting (right to left) with ones(10^0), tens(10^1), hundreds(10^2), thousands(10^3), ten thousands(10^4), etc…

BVX ECS Day 3 (1)
Class Slide from Binary Lesson – Decimal

Binary (from right to left) is one(2^0), two(2^1), four(2^2), eight(2^3), sixteen(2^4), etc…

BVX ECS Day 3
Class Slide from Binary Lesson – Binary

So “11” in binary is 3 (1 in the “2’s” place add to the 1 in the “1’s” place) and 10001 is seventeen in decimal.  There are a few tricks to read binary quicker – if the number ends in a 1, then it has a value in the 1’s place and is odd.  Also, as you add the digits together, you’ll notice that once you have “filled up” that value, you’ll need to move over to the next place value (think carrying in decimal addition) – so “111” in binary is 7, which is one less than the next place value.  “1111” in binary is 15, which is one less than the next place value. And finally “11111” is 31, which is one less than the next place value and why I thought of binary on January 31st.

Enjoying binary?  Play a binary game developed by Cisco to practice your skills! (Warning: has a rather annoying game sound – if using in class have them mute the computers first!)

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