Template:Binary Numbers
esse quam videri
Binary Numbers
As Humans we use a 10 base numbering system. For machines this numbering system is impractical.
Gottfried Willheml von Leibnitz devised the binary number system in 1679
Converting Binary Numbers
Binary->Decimal
110102 = (1 * 24) + (1 * 23) + (0 * 22) + (1 * 21) + (0 * 20) = 1610 + 810 + 0 + 210 + 0 = 2610
Dividing by two
integer | remainder | binary # |
---|---|---|
26 | ||
26/2 | 0 | 0 |
13/2 | 1 | 1 0 |
6/2 | 0 | 0 1 0 |
3/2 | 1 | 1 0 1 0 |
1/2 | 1 | 1 1 0 1 0 |
0/2 | that's it kids |
for more info see Dr. Dave's Class readings (i believe it's in week 2)Daves text
Base2
Each new bit doubles the number of intervals.
20 | =1 | monochrome, often black and white |
21 | =2 | |
22 | =4 | |
23 | =8 | Most early color Unix workstations, VGA at low resolution, Super VGA, AGA http://en.wikipedia.org/wiki/Web_colors#Web-safe_colors |
24 | =16 | |
25 | =32 | |
26 | =64 | |
27 | =128 | |
28 | =256 | |
29 | =512 | |
210 | =1024 | |
2 11 | =2048 | |
212 | =4096 | |
213 | =8192 | |
214 | =16384 | |
215 | =32768 | |
216 | =65536 | "thousands of colors" on Macintosh |
220 | =1048576 | |
224 | =16777216 | Truecolor or "millions of colors" on Macintosh systems |
232 | = 4,294,967,295 | refers to 24-bit color (Truecolor) with an additional 8 bits |
264 | = 18,446,744,073,709,551,616 | = 16 exabytes. That's more than 18 billion billion bytes. |