➕ 二进制加法计算器（多个二进制数求和）Add Binary Numbers

使用说明与常见问题How-to & FAQ

「二进制加法计算器（多个二进制数求和）」是什么？What is the Add Binary Numbers tool?

把两个或多个二进制数相加：每行一个，或用空格、逗号、加号分隔，支持很长的数（任意位数）、负数和 0b 前缀；可显示带进位的竖式，并同时给出十进制和十六进制结果，还能设置最少位数补 0、每 4 位分组。适合学习二进制加法、检查作业和数字电路练习，数据在本地处理。Add two or more binary numbers. Put one per line or separate them with spaces, commas or plus signs. Numbers of any length, negative numbers and the 0b prefix all work. Show the column addition with carries, see the result in decimal and hex too, pad to a minimum width and group every 4 bits. Handy for learning binary addition, checking homework and digital-logic exercises. Processed locally.

如何使用「二进制加法计算器（多个二进制数求和）」？How do I use the Add Binary Numbers tool?

在「二进制加法计算器（多个二进制数求和）」中，把内容粘贴或输入到上方输入框，按需设置「计算方式」、「最少位数（可选）」，结果会实时显示在下方，点击「复制结果」即可复制。例如输入「1+1+1」，得到「11」。In the Add Binary Numbers: Paste or type into the input box, adjust "Combine", "Minimum width (optional)"; the result appears below instantly — click "Copy result" to copy it. Example: "1+1+1" → "11".

怎样输入多个数？How do I enter several values?

每行一个数，或在同一行里用空格、逗号、分号或加号（+）分隔；可以带 0b 前缀，数中间的下划线会被忽略（如 1010_1100）。“自动”方式下：如果有一行包含两个以上的数，就每行单独计算；否则所有数一起计算。Put one value per line, or separate them with spaces, commas, semicolons or plus signs (+) on a line. A 0b prefix is fine and underscores inside a value are ignored (1010_1100). In Auto mode, if any line holds two or more values each line is worked out on its own; otherwise all values are combined.

二进制加法怎么进位？How does carrying work in binary?

逐位相加：0+0=0，0+1=1，1+1=10（写 0 进 1），1+1+1（含进位）=11（写 1 进 1）。勾选“显示竖式”后，两个非负数相加会显示每一位的进位；三个以上的数会逐步显示累计和。Add column by column: 0+0=0, 0+1=1, 1+1=10 (write 0, carry 1) and 1+1+1 with a carry is 11 (write 1, carry 1). With Show the working ticked, adding two non-negative numbers shows the carry above each column; with three or more values the running total is shown step by step.

可以算负数吗？Can I add negative numbers?

可以，在数前面加 - 号，例如 -101 + 11 = -10（即 -5 + 3 = -2）。结果用“负号 + 二进制”表示，不是补码；如果需要固定位数的补码运算，请先换算成补码再相加。Yes, put a minus sign in front, e.g. -101 + 11 = -10 (−5 + 3 = −2). Results use a sign and magnitude, not two's complement; for fixed-width two's-complement arithmetic convert to two's complement first.

数字有多长的限制吗？Is there a length limit?

没有固定位数限制，计算用的是任意精度整数（BigInt），几千位也能精确相加。整段输入最多 2,000,000 个字符（约几 MB）。There is no fixed bit limit; arbitrary-precision integers (BigInt) are used, so numbers thousands of bits long add exactly. The whole input is capped at 2,000,000 characters (a few MB).

计算精度如何？How precise are the results?

全程用 BigInt 任意精度整数，不是双精度浮点，所以很长的二进制加法也完全精确。All arithmetic uses BigInt (arbitrary-precision integers), not double-precision floats, so long binary additions stay exact.

输入和输出是什么样的？What does the input and output look like?

例如在「二进制加法计算器（多个二进制数求和）」中输入 1011 ⏎ 110，输出为：10001（⏎ 表示换行）。For example, the Add Binary Numbers turns the input 1011 ⏎ 110 into: 10001 (⏎ marks a line break).

有哪些选项可以调整？What options can I adjust?

「二进制加法计算器（多个二进制数求和）」的设置：「计算方式」可选 自动、所有数一起计算、每行单独计算（默认 自动）；「最少位数（可选）」可留空；可勾选：「显示竖式（含进位）」、「数中间允许空格（如 1010 1100）」、「同时显示十进制」、「同时显示十六进制」、「加 0b 前缀」、「每 4 位加空格」。改动任一选项后结果会按新设置重新生成。Settings in the Add Binary Numbers — "Combine": Auto, All values together, Each line separately (default Auto); "Minimum width (optional)" optional; tick boxes: "Show the working (with carries)", "Allow spaces inside a number (e.g. 1010 1100)", "Also show decimal", "Also show hex", "Add 0b prefix", "Space every 4 bits". Changing any option regenerates the result with the new setting.

「二进制加法计算器（多个二进制数求和）」免费吗？需要注册吗？Is the Add Binary Numbers free? Do I need an account?

「二进制加法计算器（多个二进制数求和）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Add Binary Numbers is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.