I've never understood how the Binary system works?

[jacatone]

I understand that the Binary system is 0 and 1's whereas the decimal system is based on 10, but i've never understood how numbers are represented in binary. Could someone explain how the following chart works? Thanks.


0 = 0
1 = 1
2 = 10
3 = 11
4 = 100
5 = 101
6 = 110
7 = 111
8 = 1000
9 = 1001
10 = 1010
11 = 1011
12 = 1100
13 = 1101
14 = 1110
15 = 1111
16 = 10000
17 = 10001
18 = 10010
19 = 10011
20 = 10100

[RJ]

The binary system is based on two.
So the values (from right to left), are 2^0, 2^1, 2^2 etc. And when you calculate it, you get as result 1, 2, 4, 6, 16, 32 etc.

This, like in the decimal system, goes from right to left:

256 128 64 32 16 8 4 2 1

So, let's take 1001 binary for example. You now add the corresponding decimal values, which are in this case 8+1 = 9.
And 10100 has one 1 underneath 16 and one underneath 4, and 16+4 = 20.

RJ

[Markman385]

there is also a good explenation here at pcmech under how stuff works

[Dodge7]

Think of the way out dec system works

100s 10s 1s

So, 123 = 1 2 3

123 is 1 from the hundreds col, 2 of the 10s col, and 3 from the ones col.


With binary the cols run:

8 4 2 1

so 1 0 1 0

is 8 + 2 = 10

[jacatone]

Thank you. I finally get it. So any digital medium like a DVD or a computer hard drive must have billions of these number combinations of 1 and 0's representing information or images. Correct?

[XpXJ19]

Correct. Magnetic media such as hard drives and floppy disks, use aligned magnetic particles to represent 1s and 0s, while optical media such as CD ROMs and DVD ROMs use "pits" and "lands". Light striking a land will reflect back to a light sensor, while light striking a pit will reflect away. Since there are only two options, it's binary and therefore only 1s and 0s. In the case of rewritable optical media, a laser heats the disk surface changing it's shape, which will also reflect light away and not straight back. A CD burner does not actually burn holes into a disk.

[kramer]

can someone explain it for me im confused

[kramer]

nevermind im startin to understand its just a little backwards.