使用方式
先完成一次順手的操作
- 直接點那排位元開關就能改值；1 = 亮起凸出，0 = 熄滅內凹。
- 用寬度按鈕切換 8 / 16 / 32 位元；按「取負」或 +1 看進位漣漪動畫與溢位指認。
- 切到「位移」模式同時看算術（>>）和邏輯（>>>）右移分岔；切到「位元運算」模式逐欄對齊 AND / OR / XOR / NOT。
位元實驗台Binary Bit Visualizer
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 ARow A
上方是每格的位權；最高位在二補數下是負的Column weights above; the top one is negative in two's complement
列 BRow B
結果Result
無號Unsigned
0
/
有號Signed
0
邏輯 (>>>)Logic. (>>>)
位元列 A 的五種讀法Five readings of row A
二進位Binary
Binary二進位
0000 0000
無號Unsigned
Unsigned無號
0
有號（二補數）Signed (two's complement)
Signed有號
0
十六進位Hex
Hex十六進位
00
八進位Octal
Octal八進位
0
關於位元實驗台About Binary Bit Visualizer
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.
快速導覽
使用情境、常見問題與相關工具
把需要的說明放在工具下方，讓第一次使用與之後回來複用都更順。
英文搜尋: twos complement visualizer、bit flip toggle tool、signed vs unsigned binary、arithmetic vs logical shift、int8 overflow demo、sign extension binary
常見情境
這個工具實際適合拿來做什麼
- 全 1 讀法對照（8-bit all ones）把 8 顆開關全打開（11111111）。下方拆解式直接寫出 −128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = −1 — 最高位的位權是負的，這就是同一排位元既讀 255 又讀 −1 的原因。
- 溢位現行犯：127 + 1載入 01111111 按 +1，進位漣漪一路撞進符號位元，有號讀數 127 → −128，被翻轉的 MSB 立刻被框住指認出來。
- 取負演給你看：對 8 取負載入 8（00001000）按「取負」。第一拍整排取反成 11110111，第二拍一顆冷青火花從最低位往左跑過三格、停在 bit 3，落定 11111000 = −8。−x = ~x + 1 變成看得見的動作（挑 8 不挑 5，是因為 5 的進位一步就停，看不出火花在跑）。
- 位移分身：−16 右移 1 位載入 11110000，在位移模式右移 1 位：算術（>>）得 11111000（−8），邏輯（>>>）得 01111000（120），兩列並排一目了然。
常見問題
先把常見疑問說清楚
為什麼同一排 1111 1111 又是 255 又是 −1？
位元本身沒有值，值來自讀法。無號讀法把八個 1 當純二進位＝255；二補數（有號）讀法把最高位當符號位元，1111 1111 代表 −1。位元一個都沒變，換的是怎麼讀它。
「取負」為什麼是 ~x + 1，而不是把正負號翻過來？
二補數取負的定義就是逐位取反再加一。以 5（0000 0101）為例：取反得 1111 1010，最低位 +1 得 1111 1011，那正是 −5。工具把這兩拍（取反、進位 +1）演出來，讓 −x = ~x + 1 變成看得見的動作。
int8 的 127 加 1 為什麼變成 −128？
0111 1111 加 1 時進位一路往左推，撞進最高位（符號位元），結果 1000 0000。無號讀是 128，但有號讀法看到符號位元變 1，就成了 −128。工具會把翻掉符號的那一格框起來指認出來。
>>（算術右移）和 >>>（邏輯右移）差在哪？
正數時兩者一樣；負數時分岔。算術右移補進符號位元（維持負號），邏輯右移補 0。以 1111 0000 右移 1 位為例：算術得 1111 1000（−8），邏輯得 0111 1000（120）。工具同時把兩列並排。
這跟 number-base-converter 有什麼不同？
number-base-converter 是「換算」— 你給一個值，它換成各種進位。位元實驗台是「讀法與運算」— 位元本身是輸入，你點它、對它取負/位移/做位元運算，看同一排位元在不同讀法下同時如何變化。兩支互相內鏈。
Quick guide
Use cases, answers, and nearby tools
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
Run a clean first pass
- Click any bit switch to flip it — 1 glows raised, 0 sinks recessed. Drag to flip a run of bits at once.
- Switch bit-width with the 8 / 16 / 32 buttons; hit Negate or +1 to watch the carry-ripple animation and overflow flag.
- Shift mode shows arithmetic (>>) vs. logical (>>>) right-shift side by side; Bitwise mode aligns AND / OR / XOR / NOT column by column.
Examples
Real jobs this page helps with
- All-ones dual reading (8-bit)Set all 8 switches to 1 (11111111). The decomposition line spells it out: −128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = −1. The top bit carries a NEGATIVE weight — that is why one row of bits reads as both 255 and −1.
- Overflow caught red-handed: 127 + 1Load 01111111, hit +1. The carry ripple slams the sign bit; signed jumps 127 → −128 and the MSB is framed as the culprit.
- Negate, played out: negate 8Load 8 (00001000) and press Negate. Beat one inverts the row to 11110111; beat two sends a cyan carry spark left across three cells, stopping at bit 3 to land on 11111000 = −8. That is −x = ~x + 1 as a visible action. (8 rather than 5: negating 5 stops the carry after one cell, so the spark has nowhere to travel.)
- Shift split: −16 right-shifted by 1Load 11110000, enter Shift mode, right-shift by 1. Arithmetic (>>) gives 11111000 (−8); logical (>>>) gives 01111000 (120) — shown in parallel rows.
FAQ
What people usually want to know
Why does 1111 1111 equal both 255 and −1?
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.
Why is negation ~x + 1 instead of just flipping the sign?
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.
Why does 127 + 1 become −128 in an int8?
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.
What's the difference between >> (arithmetic) and >>> (logical)?
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.
How is this different from Number Base Converter?
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.