CS 101 Web Construction, Instructor: Jeffrey Horn

Hex Numbers

(see page on BINARY NUMBERS first)

Base	Numbers
10 (decimal)	0	1	2	3	4	5	6	...	252	253	254	255
2 (binary)	00000000	00000001	00000010	00000011	00000100	00000101	00000110	...	11111100	11111101	11111110	11111111

Note how long binary numbers get, quickly.
Humans find it difficult to read and write such numbers.
So we have developed a "compromise" by using hexadecimal numbers as SHORTHAND for binary numbers.
Hex is used by HTML, so we need to know it!

System	Representation
Decimal (the actual value)	76
Binary (single byte)	01010110
Binary (2 nibbles)	0101 0110
Hex (2 hex numbers)	5 6
Hex (final html syntax)	#56

The basic idea is to break off 4 bits at a time (a nibble or nybble).
Represent each 4-bit section by a single hex symbol.(character)
This shrinks the symbol string by a factor of 4!
Makes it much easier and faster to read, write, and compare computer data without going very far from the actual representation in hardware.
BUT...we don't have enough symbols (from our base 10 alphabet) for all possible nibbles!
4 bits means we can represent 2⁴ = 16 values, from 0 to 15 (that is, 0000 to 1111).
PROBLEM: We only have 10 numerals (0..9). We need 6 more!
SOLUTION: "Steal the first 6 letters from the alphabet (A..F)

Base	Alphabet (set of symbols)
10 (decimal)	0, 1, 2, 3, 4, 5, 6, 7, 8, 9
2 (binary)	0, 1
16 (hex)	0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

Base	Numbers
10 (decimal)	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
2 (binary)	0000	0001	0010	0011	0100	0101	0110	0111	1000	1001	1010	1011	1100	1101	1110	1111
16 (hex)	0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F

Now we can represent all 16 possible values of a half of a byte (4 bits) with a single hex numeral.

System	Representation
Decimal (the actual value)	90
Binary (single byte)	01011010
Binary (2 nibbles)	0101 1010
Hex (2 hex numbers)	5 A
Hex (final html syntax)	#5A

Hex numbers are typically written as: #5A (HTML)
So #00 is smallest byte (all 0's), and #FF is largest (all ones), with #80 being about in the middle.

Language	Single Byte Numbers
JavaScript	0	1	2	...	128	...	252	253	254	255
HTML	#00	#01	#02	...	#80	...	#FC	#FD	#FE	#FF
machine code (binary)	0000 0000	0000 0001	00000010	...	1000 0000	...	1111 1100	1111 1101	1111 1110	1111 1111

For RGB, we need 3 hex numbers of two hex numerals each: #R₁R₂G₁G₂B₁B₂
So in HTML we would specify BRIGHT RED as #FF0000
So in HTML we would specify BRIGHT GREEN as #00FF00
So in HTML we would specify BRIGHT BLUE as #0000FF
Try customizing colors (to get hex number for HTML) in:
- MS Paint
- MS FrontPageu
- ```
http://johndyer.name/lab/colorpicker/  (thanks, Scott)
```

Copyright 2008 Jeff Horn. (last updated January 28, 2007) This page is URL http://cs.nmu.edu/~jeffhorn/Classes/CS101/Winter2008/hex_numbers.html