Divide hexadecimal numbers exactly, returning quotient and remainder in hex with a decimal cross-check – useful for address arithmetic and alignment calculations.
Show calculation steps
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Splitting hex quantities
Hex division returns quotient and remainder in hex — how many whole units fit, and the leftover — with decimal verification alongside. Alignment and packing problems are this operation wearing work clothes.
Powers of sixteen divide by digit-drop: ÷0x10 removes the last digit into the remainder, ÷0x100 removes two. For general divisors the exact BigInt division below does the work.
Worked example
1000 ÷ 30 Quotient: 55 Remainder: 10 Check: 0x55 × 0x30 + 0x10 = 0xFF0 + 0x10 = 0x1000 ✓ (4096 = 85 × 48 + 16)
Alignment mathematics
Remainder zero means aligned; a non-zero remainder is the misalignment, and (divisor − remainder) is the padding to the next boundary. Struct packing, DMA restrictions and allocator behaviour all reduce to reading this remainder correctly.
Truncation semantics
Quotients truncate toward zero, matching C-family integer division for positive operands. The identity q×d + r = dividend holds exactly and is printed as the check line.
Privacy
Division runs in-page; your values are not recorded.
Quotient, remainder and alignment
Hex division earns its keep in memory layout work because divisor sizes are usually powers of two, and then the quotient and remainder are just a digit split. Dividing the address 0x1234ABCD by 0x1000 gives quotient 0x1234A and remainder 0xBCD — the 4 KiB page number and the offset within that page, read straight off the digits. The remainder is also the standard alignment test: a value is aligned to a boundary exactly when dividing by that boundary leaves remainder zero. For non-power-of-two divisors the tool does exact long division, as in 0xFF ÷ 0x10 = 0xF remainder 0xF.
When the divisor is not a power of two, long division in hex runs exactly like the decimal script with a wider times table: each quotient digit is the largest of 0 through F whose product with the divisor still fits under the working remainder. The trace makes those trial digits visible for your own operands.
How to use the Hex Division Calculator
- Enter hex dividend and divisor.
- Click "Divide".
- Quotient and remainder are both shown in hex, decimal-verified.
- Zero divisors are rejected explicitly.
Frequently asked questions
What does 0x1000 ÷ 0x30 illustrate?
Quotient 0x55, remainder 0x10: 4096 = 85×48 + 16. Alignment problems look exactly like this – how many 48-byte records fit a page, and what tail remains.
Why keep the remainder in hex too?
Because the follow-on arithmetic is hex: the tail bytes after packing records, the offset within the last block. Mixed-base bookkeeping is where errors breed.
What are the classic uses?
Bytes-to-blocks conversions, records-per-page layout, alignment padding (remainder tells you the pad), and splitting address ranges into fixed-size chunks.
How does division interact with powers of 16?
Dividing by 0x10ⁿ drops n hex digits (a right shift by 4n bits); the dropped digits are the remainder. Instant mental division for power-of-16 divisors.
Is truncation toward zero used?
Yes – the integer quotient discards the fractional part, matching C-family semantics for positive operands. The remainder completes the identity dividend = quotient×divisor + remainder.
Big operands ok?
Yes – BigInt exact division at any size, e.g. a 24-digit dividend.
Local?
Fully – computed in-page, never transmitted.
