HEX HeroHow to add hexadecimal numbers
In order to add two, or more hexadecimal numbers together, you will need to know how to summarize each pair of 16 hexadecimal digits. If you don't know how to do that, take a look at the following table:
Table #1: Hexadecimal addition table
| + | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
| 0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F |
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | 10 |
| 2 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | 10 | 11 |
| 3 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | 10 | 11 | 12 |
| 4 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | 10 | 11 | 12 | 13 |
| 5 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | 10 | 11 | 12 | 13 | 14 |
| 6 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | 10 | 11 | 12 | 13 | 14 | 15 |
| 7 | 7 | 8 | 9 | A | B | C | D | E | F | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| 8 | 8 | 9 | A | B | C | D | E | F | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
| 9 | 9 | A | B | C | D | E | F | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| A | A | B | C | D | E | F | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
| B | B | C | D | E | F | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 1A |
| C | C | D | E | F | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 1A | 1B |
| D | D | E | F | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 1A | 1B | 1C |
| E | E | F | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 1A | 1B | 1C | 1D |
| F | F | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 1A | 1B | 1C | 1D | 1E |
With that out of the way, adding up two or more hexadecimal numbers is pretty easy. It really does not differ much from regular number addition in decimal numbering system. Or, any other numbering system for that matter.
Instructions:
- Line up your hexadecimal numbers
- Start from the least significant digit (rightmost)
- Add each digit using the hexadecimal addition table above
- Note down the resulting sum and carry (if any)
- Move your way up until there are no more digits to summarize
Let's see a few examples.
Example #1: Add two hexadecimal numbers - A16 and 1C
| Step description | Result |
|---|---|
| Write down 1st number | A16 |
| Write down 2nd number | 1C |
| Add one's digit: 6+C = 12, write down 2 and carry 1 | 12 |
| Add ten's digit: 1+1 = 2, plus the carried 1 = 3 | 312 |
| Add hundred's digit: A = A, since we only have one | A312 |
| Resulting hexadecimal sum | A32 |
Example #2: Add five hexadecimal numbers - A16, 1C, 33B1, 12FF5, and 2D91
| Step description | Result |
|---|---|
| Write down 1st number | A16 |
| Write down 2nd number | 1C |
| Write down 3rd number | 33B1 |
| Write down 4th number | 12FF5 |
| Write down 5th number | 2D91 |
| Add one's digit: 6+C+1+5+1 = 12+1+5+1 = 13+5+1 = 18+1 = 19, write down 9 and carry 1 | 19 |
| Add ten's digit: 1+1+B+F+9 = 2+B+F+9 = D+F+9 = 1C+9 = 25, plus the carried 1 = 26, write down 6 and carry 2 | 2619 |
| Add hundred's digit: A+3+F+D = D+F+D = 1C + D = 29, plus the carried 2 = 2B, write down B and carry 2 | 2B2619 |
| Add thousand's digit: 3+2+2 = 5+2 = 7, plus the carried 2 = 9 | 92B2619 |
| Add last digit: 1 = 1, since we only have one | 192B2619 |
| Resulting hexadecimal sum | 19B69 |
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