There's Something About Binary

How does binary work?

Computers are essentially built out of on/off switches (electricity in a wire is either "On" = 1 or "Off" = 0). Each of these binary switches is known as a "bit" and if you stick them together you can represent bigger numbers.

e.g. with 2 switches you can count 4 things (if you consider 0 to be a number):

Bit 2	Bit 1
	0	=	0
	1	=	1
1	0	=	2
1	1	=	3

Add another switch and you can count up to 8 things (7 + "0")

Bit 3	Bit 2	Bit 1
1	0	0	=	4
1	0	1	=	5
1	1	0	=	6
1	1	1	=	7

etc, etc.

Bytes

Computers generally cluster bits together into "bytes" - an 8bit computer has bytes representing numbers up to 256, but a 16bit machine can handle numbers up to 65,536 and so on.

If you have an 8 bit computer "just" counting up to 200 would be a waste of space, so that's why most figures you read around computer science utilise all the switches, i.e. are multiples of 2: "256" or "512" or "1024" etc

Hex

Writing binary out long-hand is crap, so hexadecimal was created as a shorthand.

Binary Table

Here are the first 256, 8 bit binary numbers:

0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44	45	46	47	48	49	50	51	52	53	54	55	56	57	58	59	60	61	62	63	64	65	66	67	68	69	70	71	72	73	74	75	76	77	78	79	80	81	82	83	84	85	86	87	88	89	90	91	92	93	94	95	96	97	98	99	100	101	102	103	104	105	106	107	108	109	110	111	112	113	114	115	116	117	118	119	120	121	122	123	124	125	126	127	128	129	130	131	132	133	134	135	136	137	138	139	140	141	142	143	144	145	146	147	148	149	150	151	152	153	154	155	156	157	158	159	160	161	162	163	164	165	166	167	168	169	170	171	172	173	174	175	176	177	178	179	180	181	182	183	184	185	186	187	188	189	190	191	192	193	194	195	196	197	198	199	200	201	202	203	204	205	206	207	208	209	210	211	212	213	214	215	216	217	218	219	220	221	222	223	224	225	226	227	228	229	230	231	232	233	234	235	236	237	238	239	240	241	242	243	244	245	246	247	248	249	250	251	252	253	254	255
00000000	00000001	00000001	00000011	00000001	00000101	00000011	00000111	00000001	00001001	00000101	00001101	00000011	00001011	00000111	00001111	00000001	00010001	00001001	00011001	00000101	00010101	00001101	00011101	00000011	00010011	00001011	00011011	00000111	00010111	00001111	00011111	00000001	00100001	00010001	00110001	00001001	00101001	00011001	00111001	00000101	00100101	00010101	00110101	00001101	00101101	00011101	00111101	00000011	00100011	00010011	00110011	00001011	00101011	00011011	00111011	00000111	00100111	00010111	00110111	00001111	00101111	00011111	00111111	00000001	01000001	00100001	01100001	00010001	01010001	00110001	01110001	00001001	01001001	00101001	01101001	00011001	01011001	00111001	01111001	00000101	01000101	00100101	01100101	00010101	01010101	00110101	01110101	00001101	01001101	00101101	01101101	00011101	01011101	00111101	01111101	00000011	01000011	00100011	01100011	00010011	01010011	00110011	01110011	00001011	01001011	00101011	01101011	00011011	01011011	00111011	01111011	00000111	01000111	00100111	01100111	00010111	01010111	00110111	01110111	00001111	01001111	00101111	01101111	00011111	01011111	00111111	01111111	00000001	10000001	01000001	11000001	00100001	10100001	01100001	11100001	00010001	10010001	01010001	11010001	00110001	10110001	01110001	11110001	00001001	10001001	01001001	11001001	00101001	10101001	01101001	11101001	00011001	10011001	01011001	11011001	00111001	10111001	01111001	11111001	00000101	10000101	01000101	11000101	00100101	10100101	01100101	11100101	00010101	10010101	01010101	11010101	00110101	10110101	01110101	11110101	00001101	10001101	01001101	11001101	00101101	10101101	01101101	11101101	00011101	10011101	01011101	11011101	00111101	10111101	01111101	11111101	00000011	10000011	01000011	11000011	00100011	10100011	01100011	11100011	00010011	10010011	01010011	11010011	00110011	10110011	01110011	11110011	00001011	10001011	01001011	11001011	00101011	10101011	01101011	11101011	00011011	10011011	01011011	11011011	00111011	10111011	01111011	11111011	00000111	10000111	01000111	11000111	00100111	10100111	01100111	11100111	00010111	10010111	01010111	11010111	00110111	10110111	01110111	11110111	00001111	10001111	01001111	11001111	00101111	10101111	01101111	11101111	00011111	10011111	01011111	11011111	00111111	10111111	01111111	11111111