Arithmetic right shift calculator

Choose a width, enter a signed decimal, hexadecimal, or binary integer, and specify the shift count. The result includes exact decimal values and width-padded binary patterns, making two’s-complement behavior visible without relying on a programming language’s implicit integer size or numeric limits.

Choose the signed width before shifting

An arithmetic right shift only has a precise meaning when the integer width is known. The same visible low bits can describe a positive value at one width and a negative value at another because the most significant bit is the sign bit in two’s-complement representation. Enter a width from 2 through 1024 bits, then provide a value that fits its signed range. For width w, that range begins at negative 2 raised to w minus 1 and ends at 2 raised to w minus 1, minus one. The calculator rejects values outside that range instead of silently truncating them. This makes the operation suitable for checking instruction behavior, binary protocols, compiler exercises, and code that deliberately works with fixed-size signed integers. Decimal input is often clearest for a negative number, while a 0x or 0b prefix is useful when comparing a register or packet field with documentation. The returned input pattern is padded to the chosen width, so every sign and data bit remains visible.

Understand sign extension in the result

A logical right shift always inserts zeroes on the left. An arithmetic right shift instead repeats the original sign bit: zero for a nonnegative signed value and one for a negative signed value. This repetition is called sign extension. It preserves the sign as bits move toward the least significant position. For nonnegative inputs, arithmetic and logical right shift therefore produce the same pattern. For negative inputs, they differ immediately because the arithmetic operation fills the vacated positions with ones. Numerically, shifting right by n positions behaves like division by 2 raised to n rounded toward negative infinity, not truncation toward zero. For example, negative five shifted right once becomes negative three. The output supplies both the signed decimal result and the complete width-padded result pattern, so you can verify the numeric interpretation and the bit movement together. The `sign_bit` field reports the original sign bit that was replicated, making the distinction explicit even when the shift count is zero.

Handle large shift counts and exact integers

Shift counts may range from zero through 1024. A zero count leaves the value and its bit pattern unchanged. When the count reaches or exceeds the chosen width, every original data bit has moved away; sign extension leaves zero for a nonnegative value and negative one for a negative value. This defined behavior avoids the count masking performed by some processors and languages, where a large count may be reduced modulo a machine-specific amount before execution. All integer parsing and calculation use exact arbitrary-precision integer arithmetic. Results are returned as strings because JSON numbers cannot exactly represent every integer available at widths such as 64, 128, or 1024 bits. This is intentional: consumers should parse the decimal strings with an exact integer type rather than a floating-point number. Use the binary fields when you need a direct visual comparison, and use the decimal `result` when feeding the answer into another exact calculation or a fixed-width test fixture.