Hex Arithmetic Shift Calculator
Arithmetic right-shift a hex value, preserving its sign bit — the shift mode that keeps a negative signed value negative.
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Swapnil SanghviFull-Stack Web Developer & WordPress Developer
Swapnil Sanghvi is a full-stack web and WordPress developer, UI designer, and full-time freelancer who builds and maintains Hex Calculator.
Further reading: Bitwise operation — Wikipedia
How Arithmetic Shift Works
Every bit moves right by the shift amount, and the vacated high bits are filled with a copy of the original sign bit — 1s for a negative two's-complement value, 0s for a positive one. This keeps a signed value's sign intact as it shifts, unlike logical shift.
Arithmetic Shift Example, Step by Step
0x80 >> 1 (arithmetic, 8-bit) = 0xC0
0x80 (which is -128 signed) >> 1 = 0xC0 (-64 signed)
1000 0000 (0x80, sign bit = 1) >>1, sign-extend ----------- 1100 0000 (0xC0)
| Step | Description | Result |
|---|---|---|
| Check the sign bit | 0x80 = 10000000, sign bit is 1 (negative) | fill with 1s |
| Shift right by 1 | 1000000 moves into the low 7 bits | 1000000 |
| Fill the vacated high bit with the sign bit | a 1 goes in the new top bit | 0xC0 |
0x80 as a signed 8-bit value is -128; 0xC0 is -64 — halving -128 gives -64, exactly what arithmetic shift's sign-preserving behavior is designed to do.
Where Arithmetic Shift Actually Comes Up
Dividing a Signed Value by a Power of Two
Compilers commonly translate signed integer division by a power of two into an arithmetic right shift, since it's much faster than a general division instruction.
signedValue >> 2 approximates signedValue / 4
Sign-Extending a Smaller Signed Value Into a Wider Type
Combined with a left shift first, an arithmetic right shift by the same amount sign-extends a smaller signed value correctly into a wider register.
(int8Value << 24) >> 24 sign-extends to 32-bit
Verifying Compiler-Generated Shift Instructions
When reading disassembled code, recognizing an arithmetic shift instruction (versus logical) explains why the compiler chose it — usually because the source value is a signed type.
SAR instruction (x86) = arithmetic shift right
Why Use This Calculator Instead of Doing It by Hand
- Handles the sign-bit detection and fill automatically
- Supports 8/16/32/64-bit widths, since the sign bit's position depends on width
- Runs entirely in your browser — nothing you type gets sent anywhere
- Avoids the common bug of using logical shift where arithmetic shift was needed
Limitations
- Only computes right shift — arithmetic and logical left shift are identical (always 0-fill), so there's no separate arithmetic-left mode here.
- Rounds toward negative infinity, which can differ by 1 from a language's integer division operator for negative odd values.
Frequently Asked Questions
What makes a shift "arithmetic" specifically?
Arithmetic shift fills vacated high bits with a copy of the sign bit (the most significant bit) rather than always filling with 0 — this preserves whether a signed value stays negative or positive as it shifts right.
Does arithmetic shift apply to left shifts too?
In practice, no — left shift always fills with 0 regardless of sign, so "arithmetic" vs. "logical" is only a meaningful distinction for right shifts. This calculator focuses on arithmetic right shift specifically.
Why does arithmetic right shift matter for negative numbers?
Without it, repeatedly right-shifting a two's-complement negative number using zero-fill (logical shift) would turn it into a large positive unsigned value instead of the expected smaller negative number.
Is arithmetic right shift exactly the same as dividing a negative number by 2?
Almost — arithmetic right shift rounds toward negative infinity, while integer division in most languages rounds toward zero, so the two differ by 1 for negative odd values (for example, -3 >> 1 = -2, but -3 / 2 rounds to -1 in most languages).