Numbers

As you read through these pages you might want to have a look at an ascii table. You can find one in the Banner frame ("quick links").
Conversions are very important for user interaction: If a register has the value 0x30 its corresponding ascii character is '0'. But if you want it to be displayed as '48' (0x30 is 48), you need to convert the number. In the case of '0' this is not that important, but 0xFF is displayed as a block. And '48' is better than '0' if you're displaying a temperature...
Some protocols, such as Ymodem, also use strings of values we have to convert first before we can perform calculations on them: Ymodem sends a file size of 512 bytes as '512'. An AVR has to convert this from ascii coded decimal to 16bit int first before it knows what '512' means.
Some number formats you should have in mind when doing calculations:

128 '128' 0x30 0b11001010 '11001010'

; normal decimal value ; ascii coded decimal. In this case you need three bytes ('1', '2' and ; '8') to store that number. ; hex value ; ; binary value ; ascii coded binary

It's up to you which number format you use for a specific task. Ascii coded hex is quite often used for debugging purposes, because the numbers are all of the same size (number of characters needed) and becase the conversion always takes the same number of cpu cycles and doesn't require much space. Ascii coded decimal is better for things like temperatures or rpm of a motor. Ascii coded binary is good for displaying flag registers (SREG, Interrupt flag registers and so on).
I'll show you ways to convert numbers in both directions: From int to something you can display and back.

Commonly Used Number Formats

The ALU of an AVR only knows the integer number, unsigned as well as signed, and only 8 bits wide. The 8 bit limit is not as bad, as we can still use the carry bit to make 16-, 24- and 32 bit operations possible.
Converting numbers from one format to another is not as easy and requires the person writing the code to understand the number formats first.
All conversions explained on these pages have the integer as one "end" (source or result). This is the number the AVR actually deals with.
Other formats use ASCII characters or the fact that a digit (which has a range of 0 to 9) only uses one nibble of a byte.
HEX format:
In AVR Assembler (and on this site) HEX numbers are written with the "$"-sign or "0x" at the beginning:
$10 is equal to 16 and 0x20 is equal to 32.
The Hex format splits the 8 bits of a byte into "nibbles" of 4 bits (the high nibble and the low nibble) and displays them with a number or character:

Nibble value:	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Hex:	0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F

If an 8-bit number is sent or printed as ASCII Coded Hex, the number is split into high nibble and low nibble (in the case of ox20 these are 2 and 0). Then the nibbles are converted to their ASCII representative: 0x32 for 2 and 0x30 for 0. These values can be printed on screen. The values from the table above can not be preinted on the screen: In the ASCII table these are either not defined or control characters. A won't be displayed as 'A'.
Binary format:
The binary format should be quite clear: 0b00001000 is equal to 8, 0b00011000 is equal to 24. Easy. When a number comes as ASCII coded binary, the 1s and 0s are sent as their ASCII representative, 0x30 and 0x31, and thus have to be converted before they are "real" bits. The binary format also requires bit shifting for the conversion.
Binary Coded Decimal (BCD) format:
Binary coded decimal is very handy for storing two digits (0..9) in one byte without much coding. The digits are directly written to a byte nibble.
0x22 means that the low nibble contains the number 2 and the high nibble contains the number 2 as well. A consequence of this is that a byte can only hold value in the range of 0 to 99: The values 10 to 15 (A to F in Hex format) are not allowed in BCD format.
This format can for example be written to a port which has a 7447 connected to it. This IC is a 7-segment LED driver which converts this format so that the segments of the LED display show the number of the nibble.

The Ascii Table

Very often you'll need to convert ascii to hex or decimal numbers and back. An ascii table is THE tool you'll need for that. Here is one.
If you need the hex value of 'H', look for H. It's in column $4x and row $x8. 'H' = $48 or 0x48. Other way around: You need to know what 0x69 is when shown as a character. Column $6x, row $x9: 'i'
The "ctrl" column contains the control characters in short form. The real name can be found further down on this page in a seperate table.
We're working on a printable version of this... Most probably we'll have to divide the table by three or so and fill three pages. One won't be enough for all this...

	$0x			$1x			$2x		$3x		$4x		$5x		$6x		$7x		$8x		$9x		$Ax		$Bx		$Cx		$Dx		$Ex		$Fx
	dec	char	ctrl	dec	char	ctrl	dec	char	dec	char	dec	char	dec	char	dec	char	dec	char	dec	char	dec	char	dec	char	dec	char	dec	char	dec	char	dec	char	dec	char
$x0	000		NUL	016		DLE	032	spc	048	0	064	@	080	P	096	`	112	p	128	€	144		160		176	°	192	À	208	Ð	224	à	240	ð
$x1	001		SOH	017		DC1	033	!	049	1	065	A	081	Q	097	a	113	q	129		145	‘	161	¡	177	±	193	Á	209	Ñ	225	á	241	ñ
$x2	002		STX	018		DC2	034	"	050	2	066	B	082	R	098	b	114	r	130	‚	146	’	162	¢	178	²	194	Â	210	Ò	226	â	242	ò
$x3	003		ETX	019		DC3	035	#	051	3	067	C	083	S	099	c	115	s	131	ƒ	147	“	163	£	179	³	195	Ã	211	Ó	227	ã	243	ó
$x4	004		EOT	020		DC4	036	$	052	4	068	D	084	T	100	d	116	t	132	„	148	”	164	¤	180	´	196	Ä	212	Ô	228	ä	244	ô
$x5	005		ENQ	021		NAK	037	%	053	5	069	E	085	U	101	e	117	u	133	…	149	•	165	¥	181	µ	197	Å	213	Õ	229	å	245	õ
$x6	006		ACK	022		SYN	038	&	054	6	070	F	086	V	102	f	118	v	134	†	150	–	166	¦	182	¶	198	Æ	214	Ö	230	æ	246	ö
$x7	007		BEL	023		ETB	039	'	055	7	071	G	087	W	103	g	119	w	135	‡	151	—	167	§	183	·	199	Ç	215	×	231	ç	247	÷
$x8	008		BS	024		CAN	040	(	056	8	072	H	088	X	104	h	120	x	136	ˆ	152	˜	168	¨	184	¸	200	È	216	Ø	232	è	248	ø
$x9	009		HT	025		EM	041	)	057	9	073	I	089	Y	105	i	121	y	137	‰	153	™	169	©	185	¹	201	É	217	Ù	233	é	249	ù
$xA	010		LF	026		SUB	042	*	058	:	074	J	090	Z	106	j	122	z	138	Š	154	š	170	ª	186	º	202	Ê	218	Ú	234	ê	250	ú
$xB	011		VT	027		ESC	043	+	059	;	075	K	091	[	107	k	123	{	139	‹	155	›	171	«	187	»	203	Ë	219	Û	235	ë	251	û
$xC	012		FF	028		FS	044	,	060	<	076	L	092	\	108	l	124	|	140	Œ	156	œ	172	¬	188	¼	204	Ì	220	Ü	236	ì	252	ü
$xD	013		CR	029		GS	045	-	061	=	077	M	093	]	109	m	125	}	141		157		173	­	189	½	205	Í	221	Ý	237	í	253	ý
$xE	014		SO	030		RS	046	.	062	>	078	N	094	^	110	n	126	~	142	Ž	158	ž	174	®	190	¾	206	Î	222	Þ	238	î	254	þ
$xF	015		SI	031		US	047	/	063	?	079	O	095	_	111	o	127		143		159	Ÿ	175	¯	191	¿	207	Ï	223	ß	239	ï	255	ÿ

0x20 ('spc") means space, of course.
Here is the control character table.

SOH - Start Of Header	DLE - Data Link Escape
STX - Start Of teXt	DC1 - Device Control 1
ETX - End Of teXt	DC2 - Device Control 2
EOT - End Of Transmission	DC3 - Device Control 3
ENQ - ENQuiry	DC4 - Device Control 4
ACK - ACKnowledge	NAK - Negative AcKnowledge
BEL - BELl	SYN - SYNchronous idle
BS - BackSpace	ETB - End of Transmission Block
HT - Horizontal Tabulation	CAN - CANcel
LF - Line Feed	EM - End of Medium
VT - Vertical Tabulation	SUB - SUBstitute
FF - Form Feed	ESC - ESCape
CR - Carriage Return	FS - File Separator
SO - Shift Out	GS - MainForm.Group Separator
SI - Shift In	RS - Record Separator
	US - Unit Separator