How do you add hexadecimal?

Answer 1

Hexadecimal numbers can be manipulated in exactly the same was as decimal. The digits we can use are: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. Let us take two numbers, say, 7 and 6. In decimal, we can count from 7 upward by 6... 8, 9, 10, 11, 12, 13. In Hexadecimal, we can do the same... 8, 9, A, B, C, D. Let's take two more numbers, D and 4. We count upwards from D by 4... E, F, 10, 11. Notice that after F, there is no other digit we can use, to we carry 1 to the 16's column and carry on counting to reach the final figure of 11Hex. This is just the same as the decimal procedure of carrying to the tens column after we pass 9. Once you have got your head around the idea of extra digits, the rest of it is as easy as decimal.

Answer 2

Pretty much the same way that you add decimal numbers, except that you roll over to the next digit after 7 instead of 9. 1+1 = 2 2+2 = 4 3+3 = 6 4+4 = 10 5+5 = 12 6+6 = 14 7+7 = 16 10+10 = 20 11+11 = 22 Or you can convert to decimal, add, convert back if that's easier. 11o = 1*8^1 + 1*8^0 = 9d 9+9d = 18d 18d = 22o

Answer 3

If you mean using the programming language, it'll do it automagically, for example, if you have in C:

int a = 0x389;

int b = 0x7A8;

int c = a + b;

then c will contain 0xB31 (in hexadecimal) - to display the value you would use:

printf("a + b = %X + %X = %X = c\n", a, b, c);

You can also convert to hexadecimal (for display) directly, for example:

printf("0x%x + 0x%x = 0x%x\n", 127, 207, 127 + 207);

which will display the sum in hex:

0x7f + 0xcf = 0x14e

Hex is only a convenient way to display the numbers to humans.

If you mean manually, yourself, then exactly the same way that you add in any other base.

Start at the right hand end, add the digits together and when it becomes greater than the highest digit that can be stored in a single digit, subtract multiples of the base, write the remaining digit in the answer and the number of multiples of the base subtracted is added as a carry to the next digit sum to the left.

With hexadecimal, just remember that:

0x8 + 1 = 0x9

0x9 + 1 = 0xA

0xA + 1 = 0xB

0xB + 1 = 0xC

0xC + 1 = 0xD

0xD + 1 = 0xE

0xE + 1 = 0xF

0xF + 1 = 0x10

A trick to thinking in hexadecimal is to remember that 8 is 1/2 of 16 and think of the digits above 7 as (8 + [0-7]), that is:

0x8 = (8 + 0), 0x9 = (8 + 1), 0xA = (8 + 2), 0xB = (8 + 3)

0xC = (8 + 4), 0xD = (8 + 5), 0xE = (8 + 6), 0xF = (8 + 7)

and remembering that 0x8 + 0x8 = 0x10.

Example:

0x389 + 0x7A8 = 0xB31

0x9 + 0x8 (= 8 + 1 + 8 = 0x10 + 1) = 0x11 = 0x1 carry 1

0x8 + 0xA + carry 1 (= 8 + 8 + 2 + 1 = 0x10 + 3) = 0x13 = 0x3 carry 1

0x3 + 0x7 + carry 1 (= 8 + 3) = 0xB

If you can't think using the fifteen single digits, work in decimal remembering the conversions:

0xA = 10

0xB = 11

0xC = 12

0xD = 13

0xE = 14

0xF = 15

For example the second addition above becomes:

0x8 + 0xA + carry 1 = 8 + 10 + 1 = 19 (= 16 + 3 = 0x10 + 3) = 0x13 = 0x3 carry 1