Hex Addition: How to Add Hexadecimal Numbers with Examples

Hex addition works like ordinary column addition, but hexadecimal is base 16. Digits A-F stand for decimal 10-15, and a column carries into the next one once its total reaches decimal 16 instead of decimal 10. That single difference is what makes F₁₆ + 1₁₆ = 10₁₆ — not "ten," but the hex way of writing decimal sixteen.

This guide covers the hex digit values, the carrying rule that drives every hex addition, a full addition table, and several worked examples verified column by column, from a simple sum with no carrying to one with cascading carries.

What Is Hexadecimal Addition?

Hexadecimal addition is arithmetic performed in base 16, where every number is written using sixteen digit symbols: 0 through 9, then A through F for the values that a single 0-9 digit can't hold. Each position in a hex number represents a power of 16 — 1, 16, 256, 4096, and so on — the same positional-notation idea decimal uses with powers of 10.

Like decimal addition, hex addition proceeds one column at a time, starting from the rightmost digit and moving left. The mechanics are identical to decimal; only the carry threshold changes. For the full place-value breakdown behind this, see how to convert hex to decimal.

Hexadecimal Digit Values

Before adding hex numbers, it helps to have the digit-to-decimal mapping memorized, since every column addition depends on it:

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

After F, hexadecimal runs out of single-digit symbols. The next number is written 10₁₆, and that represents decimal 16 — not decimal ten. This rollover is the entire basis for carrying in hex addition.

Uppercase and lowercase letters represent the same values: A and a are both 10, F and f are both 15. This article uses uppercase, matching the Hex Converter's display convention.

Hexadecimal Addition Rules

The core rule: decimal addition carries when a column reaches 10; hexadecimal addition carries when a column reaches decimal 16.

For a column with decimal total S:

digit written = S mod 16
carry         = floor(S / 16)

If S is below 16, the digit written is just S converted to hex, with no carry. If S is 16 or greater, subtract 16 to get the digit (converting 10-15 back to A-F), and carry 1 into the next column.

The simplest possible demonstration is F₁₆ + 1₁₆:

F + 1 = 15 + 1 = 16 decimal = 10 hex

Write 0, carry 1 — giving F₁₆ + 1₁₆ = 10₁₆.

Putting the full method together:

1. Align the two hex numbers by their rightmost (least significant) digit.
2. Start at the rightmost column.
3. Convert any A-F digits to their decimal values.
4. Add both digits in the column, plus any carry from the column to the right.
5. If the total is below decimal 16, write its hex equivalent directly.
6. If the total is 16 or greater, subtract 16 to get the digit, convert it to A-F if needed, and carry 1 into the next column.
7. Move one column left and repeat.
8. After the leftmost column, if a carry remains, write it as a new leading digit.
9. Confirm every digit in the final answer is one of 0-9 or A-F.

Hex Addition Table

For any two single hex digits, here's the complete sum — every one of the 256 possible combinations, verified programmatically and displayed in hexadecimal. Find one digit in the left column and the other across the top; the cell where they meet is the hex sum.

A few entries worth double-checking by hand: 1 + F = 10, A + 5 = F, A + A = 14, and F + F = 1E — all four match the table above.

How to Add Hexadecimal Numbers Step by Step

The table above only covers single digits. For numbers with more than one digit, apply the same rule column by column:

1. Write the two hex numbers with their rightmost digits aligned.
2. Add the rightmost column, converting any A-F digits to decimal first.
3. If the total is under 16, write its hex digit and move on with no carry.
4. If the total is 16 or more, write (total − 16) in hex and carry 1 into the next column.
5. Repeat for each column moving left, always including any carry from the previous column.
6. If a carry is left over after the final column, write it as a new leading digit.

Example Without Carrying

23₁₆ + 14₁₆

  23
+ 14
----
  37

• Rightmost column: 3 + 4 = 7 (no carry)
• Next column: 2 + 1 = 3 (no carry)

Result: 37₁₆

Decimal check: 23₁₆ = 35, 14₁₆ = 20, and 35 + 20 = 55. 37₁₆ = (3 × 16) + 7 = 48 + 7 = 55. The two totals match, so the addition is correct.

Example With Carrying: 2F + 1D

2F₁₆ + 1D₁₆

  2F
+ 1D
----
  4C

• Rightmost column: F + D = 15 + 13 = 28 decimal. 28 is 16 or more, so subtract 16 to get 12, which is C in hex. Write C, carry 1.
• Next column: 2 + 1 + the carried 1 = 4. 4 is under 16, so write 4 directly.

Result: 4C₁₆

Decimal check: 2F₁₆ = (2 × 16) + 15 = 47. 1D₁₆ = (1 × 16) + 13 = 29. 47 + 29 = 76. And 4C₁₆ = (4 × 16) + 12 = 64 + 12 = 76. Both totals agree: 2F₁₆ + 1D₁₆ = 4C₁₆.

Hex Addition With Multiple Carries

A7₁₆ + 5D₁₆

  A7
+ 5D
----
 104

Walking through each column:

Column	Digit 1	Digit 2	Carry in	Decimal total	Hex total	Digit written	Carry out
Rightmost	7	D (13)	0	20	14	4	1
Middle	A (10)	5	1	16	10	0	1
Final carry	—	—	1	—	—	1	—

• Rightmost column: 7 + 13 + 0 = 20 decimal = 14 hex. Write 4, carry 1.
• Next column: 10 + 5 + 1 = 16 decimal = 10 hex. Write 0, carry 1.
• No columns remain, so the leftover carry becomes a new leading digit: 1.

Reading the leading carry followed by each column's digit gives 104₁₆.

Decimal check: A7₁₆ = (10 × 16) + 7 = 167. 5D₁₆ = (5 × 16) + 13 = 93. 167 + 93 = 260. And 104₁₆ = (1 × 256) + (0 × 16) + 4 = 260. Both totals agree: A7₁₆ + 5D₁₆ = 104₁₆.

This example shows why carries can cascade: the first column's carry pushed the second column's total to exactly 16, which triggered a second carry — and that second carry had nowhere to go but a brand-new digit.

Why Do You Carry at 16 in Hexadecimal?

Hexadecimal has sixteen digit values, 0 through F, and no single digit for the value after F. The next number simply has to roll into a new column: 16₁₀ = 10₁₆.

The same rollover keeps happening one number at a time:

17 decimal = 11 hex
18 decimal = 12 hex
19 decimal = 13 hex
...
31 decimal = 1F hex
32 decimal = 20 hex

This is the exact same mechanism as decimal running out of digits after 9 and rolling into 10, or octal running out after 7 and rolling into 10₈ (as covered in how to convert octal to hexadecimal). Every positional number system carries the moment a column's value reaches its base — hexadecimal's base is just 16 instead of 10.

Hexadecimal vs Decimal Addition

	Decimal	Hexadecimal
Base	10	16
Digits available	0-9	0-9, A-F
Carry triggers at column total of	10	16
Example	9 + 1 = 10	F + 1 = 10

The critical thing to remember: 10₁₆ does not mean decimal ten. It's hexadecimal's way of writing decimal sixteen, the same way decimal's "10" is just the way ten gets written once a single digit can't hold it. Reading a hex result as if it were decimal is one of the most common sources of mistakes, covered more below.

How to Check a Hex Addition Answer

The most reliable way to verify a hex sum is to redo the arithmetic in decimal:

1. Convert each hex operand to decimal.
2. Add the decimal values.
3. Convert your hex result to decimal (or convert the decimal sum back to hex).
4. Confirm both totals match.

Using the earlier example:

2F16 = 47
1D16 = 29
47 + 29 = 76
4C16 = 76

Both sides equal 76, confirming 2F₁₆ + 1D₁₆ = 4C₁₆. For longer numbers, the Hex to Decimal Converter and Decimal to Hex Converter make this check quick without doing the place-value math by hand.

Common Hex Addition Mistakes

• Carrying at 10 instead of 16. This is the single most common slip — a habit carried over from decimal that produces a wrong digit and a wrong carry.
• Forgetting that A-F stand for 10-15. Adding hex digits as if they were letters instead of numbers, rather than converting them to their decimal values first.
• Reading a hex result as decimal. 10₁₆ means decimal 16, not decimal ten — the digits alone don't reveal the base without context.
• Dropping an incoming carry. Once a column produces a carry, it must be added into the next column; skipping it changes every digit after it.
• Writing a decimal total directly into the answer. A column total like 28 has to be converted to its hex digit (C, with a carry) — it can never appear as "28" in a hex result.
• Forgetting to convert 10-15 back to A-F. After computing a column's digit value, a result like 12 needs to be written as C, not left as the number 12.
• Misaligning place values. Numbers of different lengths must be lined up by their rightmost digit, not their leftmost one.
• Dropping the final carry. If a carry remains after the leftmost column, it becomes a new leading digit — omitting it leaves the answer one digit short.

Frequently Asked Questions

What is hex addition?

Hex addition is column addition performed in base 16 (hexadecimal), the number system that uses sixteen digits: 0-9 and A-F, where A-F stand for decimal 10-15. It works exactly like decimal addition, except a column carries into the next one once its total reaches decimal 16 instead of 10.

How do you add hexadecimal numbers?

Align the two hex numbers by their rightmost digit, then add column by column from right to left. Add the two digits in a column (converting any A-F to its decimal value first) plus any incoming carry, write the hexadecimal digit for that total, and carry 1 into the next column whenever the total is 16 or greater. If a carry remains after the leftmost column, write it as a new leading digit.

What are the rules for hexadecimal addition?

For any column total S (in decimal), the digit written is S mod 16 and the carry is floor(S divided by 16). If S is less than 16, write its hex equivalent directly with no carry. If S is 16 or greater, subtract 16 to get the digit and carry 1. Convert any result from 10-15 back into A-F before writing it down.

Why does F plus 1 equal 10 in hexadecimal?

F is the last hexadecimal digit, standing for decimal 15. Adding 1 gives decimal 16, and hexadecimal has no single digit for 16 — the same way decimal has no single digit for ten. So the result rolls over: write 0 in the current column and carry 1, giving 10 in hex, which represents decimal 16, not decimal ten.

What do A, B, C, D, E, and F mean in hexadecimal?

They are single hex digits standing for decimal values that a lone 0-9 digit can't represent: A=10, B=11, C=12, D=13, E=14, F=15. Hexadecimal needs these six extra symbols because it's a base-16 system with sixteen possible digit values per position.

What is 2F plus 1D in hexadecimal?

2F₁₆ + 1D₁₆ = 4C₁₆. In the rightmost column, F + D = 15 + 13 = 28 decimal, which is 1C in hex, so you write C and carry 1. In the next column, 2 + 1 + the carried 1 = 4. Checked in decimal: 2F₁₆ is 47, 1D₁₆ is 29, and 47 + 29 = 76, which equals 4C₁₆.

How do you check a hexadecimal addition answer?

Convert both hex operands to decimal, add the decimal values, then convert that decimal sum back to hex (or convert your hex result to decimal) and compare. If both totals match, the addition is correct. The Hex to Decimal Converter and Decimal to Hex Converter make this check quick for longer numbers.

Is hex addition the same as decimal addition?

The process is identical — align by place value, add column by column from the right, carry when a column overflows. The only difference is where the overflow point sits: decimal carries at a column total of 10, hexadecimal carries at a column total of 16.