Carry at sixteen
Hex Addition Calculator
Add two hexadecimal values, with the carry rule and column-by-column working explained.
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The one rule that changes
Hex addition is decimal addition with a different overflow point. A column carries when it reaches sixteen, not ten. Everything else — align right, work right to left, carry into the next column — is unchanged.
| Decimal thinking | Hex reality |
|---|---|
| 9 + 1 = 10, carry | F + 1 = 10, carry |
| A column holds 0–9 | A column holds 0–F |
| Carry means +10 | Carry means +16 |
| Borrow takes 10 | Borrow takes 16 |
Adding two digits
Every single-digit hex addition falls into one of two cases.
sum below 16 → write it, no carry
7 + 5 = 12 = C
sum 16 or more → subtract 16, carry 1
9 + B = 9 + 11 = 20
20 - 16 = 4
→ write 4, carry 1
Full worked example
1A2B + 0C3D ------ ones: B + D = 11 + 13 = 24 = 16 + 8 → 8, carry 1 16s: 2 + 3 + 1 = 6 → 6 256s: A + C = 10 + 12 = 22 = 16 + 6 → 6, carry 1 4096s: 1 + 0 + 1 = 2 → 2 result → 2668 (6699 + 3133 = 9832 in decimal)
Additions worth memorising
These come up constantly when working with byte values and masks.
| Sum | Result | Decimal |
|---|---|---|
| F + 1 | 10 | 15 + 1 = 16 |
| F + F | 1E | 15 + 15 = 30 |
| FF + 1 | 100 | 255 + 1 = 256 |
| 80 + 80 | 100 | 128 + 128 = 256 |
| 0F + 01 | 10 | 15 + 1 = 16 |
| FFFF + 1 | 10000 | 65,535 + 1 = 65,536 |
The pattern is worth noticing: adding 1 to a run of Fs always rolls over to a
1 followed by zeros, exactly as adding 1 to a run of 9s does in decimal.
Fixed-width addition
Hardware cannot produce a longer answer than the register it is using. When a carry falls off the top it is simply lost, and the result wraps.
8-bit register
FF + 01 = 100 → only 2 digits fit → result 00, carry flag set
7F + 01 = 80 → fits, but the sign bit flipped
(127 + 1 = -128 if signed)
This calculator does not wrap — it gives the mathematically exact answer. To model an n-bit register, keep the last n/4 hex digits.
Frequently asked questions
How do I add hexadecimal numbers?
Align them on the right and add column by column, carrying whenever a column reaches sixteen instead of ten.
What is F + 1 in hex?
10, which means sixteen. It is the same rollover as 9 + 1 in decimal.
What is FF + 1?
100 in hex, or 256 in decimal. In a fixed 8-bit register it wraps to 00 and sets the carry flag.
When do I carry in hex addition?
Whenever a column total reaches 16 or more. Subtract 16 from the total and carry 1.
Can I add hex and decimal numbers together?
Convert one to the other's base first. Mixing notations in a single column is where mistakes come from.
Does this calculator wrap on overflow?
No. It gives the exact result with no width limit. Keep the last two digits for 8-bit, four for 16-bit, eight for 32-bit.