Number Systems and Bases

@Anon: Great point. Yep, hex is a good shorthand, and oftentimes I have to explicitly separate out the hex digits to see what’s happening with a bitmask.

You might also mention that hexadecimal originated as a convenient way to condense binary into groups of four digits. When I teach people what binary and hex are, I start with binary, and at some point start grouping the digits into fours, and then explain that these 16 combinations could be represented with a single character, and hence hex was born. (If introducing octal, I group in 3’s first, because people are already familiar with octal’s digits.)

Really silly, but can we have have an base root-1, or i?

@Bwire: Thanks, glad it helped.

Great explanation that’s easy to understand. I now understand the number systems well. Thank you.

I drop a leave a response when I like a post on a website or I have something to contribute
to the conversation. It’s a result of the passion communicated in the article I looked at. And on this post Number Systems and Bases | BetterExplained. I was actually moved enough to drop a comment :slight_smile: I do have a few questions for you if it’s okay.
Could it be simply me or does it appear like some of these comments come across as if
they are left by brain dead people? :stuck_out_tongue: And, if you are posting at other social sites,
I’d like to follow you. Could you make a list all of all your social pages like your twitter feed, Facebook page or linkedin profile?

How to change base system to decimal?

I appreciate the information on this website, but could you possibly help me further? I have a midterm and my teacher expects us to be able to write a table for either addition or multiplication for a base (seven, five, sixteen, etc…) in order to answer problems that will be on the midterm. Thank you in advance for your help!

Hi Kris, thanks for the suggestion. Added to my topic list.

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can anyone please tell that how many base number systems do we have?? plese tell

thank you for giving a such a valuable information and i have a doubt that why object codes are stored in hexa decimal number system in c programming

Great lessons overall, will you prepare something on power law? Pareto, poison distributions etc?

Thanks for this article. I am doing research on the Babylonian sexagesamil (60 base) time system. I was struggling to understand what a base system was. All the articles kept referring to it without fully explaining. I will be adding this as a Math lesson for my students to play with in addition to their regular Math lessons. I am excited to show them another way that History and Math are linked together!!
Quick question: I didn’t look, but did you do that separate article about the binary system as asked in the comments? Could you save me a little time and post the link? Thanks so much. I greatly appreciate it.

@Co Op: Thanks, glad it helped! Always happy to provide analogies for other teachers to use ;).

I have an article on binary as used by computers, hope it helps: http://betterexplained.com/articles/a-little-diddy-about-binary-file-formats/

Sincerely speaking, i seem nt 2 understand d idea in “tick over”. Also, can u pls help me wit d names f d system and their representation, eg Base 2 - Binary - 0,1. Thnks in advance.

Sincerely speaking, i seem nt 2 understand d idea in “tick over”. Also, can u pls help me wit d names f d system and their representation, eg Base 2 - Binary - 0,1. Thanks in advance.

say about history of number system

For those who need a bit more help,
Think of it this way:
If you count to ten using you fingers, the first finger to come up represents 1. If you continue counting, you will reach 10, which represents a complete set; you have no other fingers to continue counting.

In order to continue, you must clench both hands into fists in order to start again with the next set, ie. 11, 12, 13… . This is why it is called the Base 10 system and not the Base 9 system.

The number 10 represents a complete set of the base 10 system. When you count 7,8,9- the next number is the final, finishing touch to the set. It is 1 and 0, meaning 1 set, and 0 more, 10. If we continue, it continues saying, “1 set and 1 more,” “1 set and 2 more,” eventually reaching 19, which should continue into “2 sets, and 0 more.”

Also, 0 is a number, it is in fact even. Picture this:
Imagine a scale, when it has nothing on it, the scale is perfectly balanced, even.
Now, place 1 item on either side, it is now uneven (odd).
Now, place 1 more item equal in weight (2 total) on the opposing side, it is even again.
If you reached 9 objects, the scales would be uneven, the 2 sides would have different amounts. When you look at both your hands, you should have an even number of fingers in total, 5 and 5 making an even 10.

----For those who want more, I’m moving onto Base 12----
This is my favourite of all the bases. There are many reasons why I love Base 12, but one of the easiest to see is simple division.
You see, when we like to divide, we like simple numbers, not decimals, only whole (2, not 1.6666…).
Carpenters know this very well, since they use the imperial system (it has problems of it’s own, but it does use base 12).
Imagine this:
Base 12: put down 12 objects on the table, put it into 2 equal piles.
how many do you have in each? 6.
Now put down 12 objects again, put it into 4 equal piles.
How many? 3.
Put down the 12 one last time, cut them into 3 equal piles.
How many now? 4.

Base 10: put down 10 objects on the table, put it into 2 equal piles.
how many do you have in each? 5.
Now put down 10 objects again, put it into 4 equal piles.
How many? You can’t you need to cut 2 of them in half, making 4 halves, then distribute them amongst all 4, making each pile 2 and a half, or 2.5, ewwww.
Put down the 10 one last time, cut them into 3 equal piles.
How many now? This one is insanity, you have to cut 1 of them into 3 equal pieces, which is really difficult to do since you have to use angles to figure out the equally distributed, 120 degree slices, how much is a third again? oh yeah its .33333333… repeated, you can never have a perfect number to work with, it’s always going to be wrong, with 10 cut into 3 piles, you end up with 3 and 1 third, or 3.3333333333… .

Anyways, that’s just division, if you are interested in a diagram of why I love base 12, just look at this picture I made: http://prntscr.com/3wladb
I really hope humanity educates ourselves to base 12, it would be beautiful.

Just reading your piece on number bases and understand most of it except this which makes no sense.

1: 1 2: 10 (we’re full – tick over) 3: 11 4: 100 (we’re full again – tick over) 5: 101 6: 110 7: 111 8: 1000 (tick over a

In school I had no problem and had great fun messing with number bases but the above???

Regards

Frank

PS I’ve returned to maths!