Instructor: Jeffrey Horn

Binary Numbers

Minimum alphabet (2 numerals)
What actual computer hardware uses (bits):
- "0" - off
- "1" - on
- typically, "0" is represented by 0 volts, while "1" is represented by 5 volts (or 3 volts, in VLSI circuits).
- Binary representation makes circuits easier to design and build. (But not necessary!)
Can represent any number, just using 0s and 1s!

Note how we have to use more "places" to represent numbers in binary than in decimal. This is the consequence of the smaller alphabet.

In particular, if we have 8 bits (a byte) then we can represent 2⁸ = 256 different numbers.
Since we start with 0, we can count as high as 255 using only 8 bits (and NOT 256!).

For example, in HTML, JavaScript, Java, and many other languages, the RGB (red,green,blue) color coordinate system is used to specify colors, with a single BYTE for each of the RGB values.
Thus these are known as 24-bit color systems.
Each color component (RGB) uses a single byte, and so can take on any of 256 different values, from 00000000 (no contribution from that color) to 1111111 (full contribution of that color).
The combination of the three color components determines the final color. Thus an RGB setting of (11111111,00000000,1111111) for (R,G,B) would be bright purple. This would be (255,0,255) in Java and in JavaScript. Note that 255 is the maximum decimal value for a color component.
What color would (1111111111,11111111,11111111) = (255,255,255) give?
What about would (00000000,00000000,00000000) = (0,0,0) give?
What about (x,x,x), where x is any value? (i.e., all three components are the same value)
Note that any numbers other than 0..255 (such as negative numbers, or even 256) are NOT valid and can cause errors in your code and on your page!

The way to specify colors in this systems is with three numbers for the three components: (0..255, 0,255, 0..255) for (R,G,B).
Total number of combinations with 24-bit color = 256 * 256 * 256 = 2⁸ * 2⁸ * 2⁸ = 2²⁴ = 16, 777, 216 ≈ 16 Meg!
16 Million colors is plenty (for now!).

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