How to Learn / Do Binary / Base 2 / Base Two Number System (0's and 1's). Learning Mathematics. Math Examples.
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How to Learn Binary / Base 2 Number System: Introduction
Binary is the basis of all digital technology; strings of 1’s and 0’s. The different combinations of 1’s and 0’s are how the technology tells itself what to do.
If you understand the decimal (base 10) number system that you use every day, then you already understand the binary (base 2) number system. You just don’t know that you know yet.
How to Learn Binary / Base 2 Number System: Tutorial
We use the decimal (base 10) number system in our day-to-day living. Base 10 has ten numbers (0-9) and orders of magnitude that are times ten. The lowest-order number represents itself times one. The next-order number represents itself times ten. The next order number represents itself times 10x10 or itself times 100. The next order number represents itself times 10x10x10 or itself times 1000. And so on.
An example would be the number 497. This number means that there are:
Seven 1’s,
nine 10’s,
and four 100’s.
Which represents 7 +90 +400; for a total of 497.
The binary (base 2) number system (0's and 1's)...
...uses the same structure, the only difference being the order of magnitude. Base 2 has two numbers (0-1) and orders of magnitude that are times two. The lowest-order number represents itself times one. The next-order number represents itself times two. The next order number represents itself times 2x2 or itself times 4. The next order number represents itself times 2x2x2 or itself times 8. The next order number represents itself as 2x2x2x2 or itself times 16, And so on.
An example would be the number 10110. This number means that there are:
No 1’s,
one 2’s,
one 4’s,
no 8’s,
and one 16.
Which represents 0 + 2 + 4 + 0 + 16; for a total of 22.
Other binary (base 2) examples are:
0=0
1=1
10=2
11=3
100=4
101=5
110=6
111=7
1000=8
1001=9
1010=10
1011=11
1100=12
1101=13
1110=14
1111=15
10000=16
[All about pi and Pi Day. Comes up on the 14th of March every year. Has pi in binary format.]
Other Base Number Systems and Math Tutorials / Examples
CommentsLoading...
This is very useful.Congratulations
paradigm,
I forgot what I learned 30 years ago. It feels good for the awakening. I love your galaxy pictures. I'll have to revisit my past to recover what I lost. Thanks.
Ronnie
Pcunix Level 7 Commenter 20 months ago
If you Google for "Javascript Bit Twiddler" you will find a page of mine where you can set binary bits with your mouse (or finger on an iPad etc.) and immediately see the value in decimal, octal and hex. The code is available there also.
I hope you think that is useful, but if not, just delete the comment and I understand.