Hex Numbering

Hex is the numbering system most used by computer programmers. There are a lot of reasons why hex is so popular.

This document will explain what the Hex numbering system is, and how it applies.

In Hex there are 16 relevant characters that make up the numbering system. This is also called a base 16 numbering system.

The digits in the Hex number system are:

0 1 2 3 4 5 6 7 8 9 A B C D E F

Decimal (our standard, base 10, number system) uses only 0 through 9, therefore the letters are necessary. You can convert between decimal and hex fairly easily. The way Hex relates to Decimal can be illustrated as:

			Second digit
			Hex
			0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F
F i r s t D i g i t	H e x	0	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
		1	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31
		2	32	33	34	35	36	37	38	39	40	41	42	43	44	45	46	47
		3	48	49	50	51	52	53	54	55	56	57	58	59	60	61	62	63
		4	64	65	66	67	68	69	70	71	72	73	74	75	76	77	78	79
		5	80	81	82	83	84	85	86	87	88	89	90	91	92	93	94	95
		6	96	97	98	99	100	101	102	103	104	105	106	107	108	109	110	111
		7	112	113	114	115	116	117	118	119	120	121	122	123	124	125	126	127
		8	128	129	130	131	132	133	134	135	136	137	138	139	140	141	142	143
		9	144	145	146	147	148	149	150	151	152	153	154	155	156	157	158	159
		A	160	161	162	163	164	165	166	167	168	169	170	171	172	173	174	175
		B	176	177	178	179	180	181	182	183	184	185	186	187	188	189	190	191
		C	192	193	194	195	196	197	198	199	200	201	202	203	204	205	206	207
		D	208	209	210	211	212	213	214	215	216	217	218	219	220	221	222	223
		E	224	225	226	227	228	229	230	231	232	233	234	235	236	237	238	239
		F	240	241	242	243	244	245	246	247	248	249	250	251	252	253	254	255

Hex is primarily used because It can easily represent several different numbers. In hex, You will only need 6 digits to represent a color code, because the number represents all the possible combinations of color codes. This relates directly to how computers store numbers, specifically how big each number can be per a unit of memory. Most computers have a standard unit system for storing information. This is a byte. It represents 8 "bits" which can be either 0 or 1. There are 256 possible combinations of bits in a byte. Each Hex digit corresponds to 4 binary bits, this means that 2 Hex digits can represent 8 bits. Here is a table of how Hex relates to Binary:

Hex	0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F
Binary	0000	0001	0010	0011	0100	0101	0110	0111	1000	1001	1010	1011	1100	1101	1110	1111

As you can see, Hex can be used to easily represent bit patterns. The reason Hex is used most often is because it can represent large numbers in a visually compact format.