點一排位元開關，無號、二補數、十六進位讀數同時翻動 — 位元沒變，變的是讀法。Flip a bit — watch unsigned, signed (two's complement), hex, and octal update at once.
位元列 A 的五種讀法Five readings of row A
位元本身沒有值，有值的是讀法。同一排 1111 1111，用無號讀法讀是 255；用二補數（有號）讀法讀是 −1。位元一個都沒動，換的是怎麼讀它。這個工具讓位元列成為唯一的真相來源：點下去就翻，底下所有讀法同時跟著更新。Bits have no intrinsic value — the interpretation does. The same pattern 1111 1111 reads as 255 in unsigned and −1 in two's complement (signed). Not a single bit changed; only the reading rule did. This tool makes the bit row the single source of truth: click a bit to flip it, and all four readouts update in the same visual beat.
「取負」操作演示二補數的 −x = ~x + 1 定義：先全部位元取反（~x），再從最低位加一，進位從右向左漣波直到遇見第一個 0 位元停下。工具把這兩拍分開演出：第一拍整排瞬間取反，第二拍一顆冷青火花沿位元列橫向推進。當操作使符號位元（最高位）意外翻轉，有號讀數突變正負，那一格會被框住指認出來。The "Negate" operation demonstrates the two's complement rule −x = ~x + 1: first invert all bits, then add 1 from the LSB, rippling carry leftward until it hits a 0. The tool plays this in two distinct beats: all bits invert at once, then a cyan carry spark travels the row bit by bit. If the carry flips the sign bit (MSB) unexpectedly — causing signed overflow — that cell is framed and highlighted.
32 位元模式的所有讀法一律以 BigInt 計算，完全繞開 JavaScript 位元運算子 32 位有號的限制（例如 1 << 31 在 JS 會是負數）。邏輯右移（>>>）在 8/16 位元模式下以無號遮罩手算，保持語意正確。術語對照：二補數、符號位元、最高位元（MSB）、算術右移（>>）、邏輯右移（>>>）、符號延伸、溢位、進位漣波。All 32-bit readouts use BigInt, bypassing JavaScript's 32-bit signed-integer trap (e.g. 1 << 31 becoming negative). Logical right shift (>>>) in 8/16-bit modes is computed via an unsigned mask. Glossary: two's complement, sign bit, MSB, arithmetic right shift (>>), logical right shift (>>>), sign extension, overflow, carry ripple.
Quick guide
Compact below-tool notes that help first-run users and repeated visitors move faster without changing the main interface.
Chinese search: 二補數 計算、位元 視覺化、int8 溢位、算術右移 邏輯右移 差別、符號位元 溢位、補數 取負 演示
How to use
Examples
FAQ
Bits have no inherent value — the reading rule does. Unsigned treats all eight 1s as pure binary = 255. Two's complement (signed) treats the MSB as a sign bit, making 1111 1111 equal −1. Not a single bit changed; only the interpretation did.
Two's complement defines negation as bitwise NOT then add 1. Take 5 (0000 0101): invert to get 1111 1010, add 1 to get 1111 1011, which is −5. The tool plays both beats — invert, then carry ripple — so −x = ~x + 1 becomes a visible action.
Adding 1 to 0111 1111 carries all the way into the sign bit, producing 1000 0000. Unsigned reads 128, but signed sees a 1 in the MSB and reads −128. The tool frames the flipped bit as the overflow culprit.
Identical for positive numbers; they diverge for negatives. Arithmetic shift fills the vacated high bits with the sign bit (preserving the sign); logical shift fills with 0s. Right-shifting 1111 0000 by 1: arithmetic → 1111 1000 (−8), logical → 0111 1000 (120). The tool shows both rows in parallel.
Number Base Converter is about conversion — give it a value, get it in different bases. Binary Bit Visualizer is about interpretation and operations — bits are the input, and you flip them, negate them, shift them, and run bitwise ops on them, watching all four readings update in the same instant.