RTCM v11-22-99

Help with HEX

Hexadecimal number format:

If you don't know the hexadecimal number format, here's a short description.

The everyday decimal number notation is base 10. That means there are
10 different symbols (0,1,2,3,4,5,6,7,8,9) that are strung together to
make a number. A given digit in a number has 10 times the value it would 
have if it was one place to the right.

The hexadecimal number notation is base 16. It has 16 different symbols:
0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. These digits in decimal would be 0 through 15.
A given digit in a hex (short for hexadecimal) number has 16 times the value
it would have if it was one place to the right.

To convert hex to decimal, multiply the value of each digit (0 to 15) by 16 
raised to the power of its place (rightmost place = 0), and add the results 
together.
For example, 15F (hex) would be (1*256) + (5*16) + (15*1) = 351

To convert decimal to hex, divide the decimal number by an appropriate hex
place value (1,16,256,4096,65536 etc.) to get a hex digit (ignore the part
that is < 0) and subtract the decimal value of this digit*place from the
decimal number. For example: 1000 (decimal) would be:
(1000/256)            = 3.906    = 3         = 3
((1000 - (3*256))/16) = (232/16) = 14.5 = 14 = E
((232 - (14*16))/1)   = (8/1)    = 8         = 8
Therefore, 1000 decimal is 3E8 hexadecimal.

Conversion between hex and binary, simply substitute four-bit groups for
the hex digit of the same value. Specifically: 
Hex Digit:  0  1  2  3  4  5  6  7  
Bit Group:  0000  0001  0010  0011  0100  0101  0110  0111  

Hex Digit:  8  9  a  b  c  d  e  f  
Bit Group:  1000  1001  1010  1011  1100  1101  1110  1111  


For conversion from hex to binary, simply string together the bits for
each hex digit. For instance, 0x509d7a is binary 10100001001110101111010.
To wit: 

Hex Number:  5  0  9  d  7  a  
Binary Number:  0101  0000  1001  1101  0111  1010  


To convert the other way, break the binary number into groups of four,
then replace each one with its hex digit. Group the digits starting from
the right. If you don't have a complete group of four when you reach the
left, pad with zero bits on the left to fill the last group. For instance,
binary 111011011111110001 is 0x3b7f1: 

Binary Groups:  0011  1011  0111  1111  0001  
Hex Digits:  3  b  7  f  1  


Because this conversion is so easy, the easiest way to convert between binary
and decimal is usually to go through hex. It generally requires fewer operations,
and hex numbers are easier to work with because they are shorter Also, it's easier
to remember where you are when scanning a hex number, since the digits differ more. 

Complicated, A calculator will help you.