✖️ 二进制乘法计算器（多个二进制数相乘）Multiply Binary Numbers
把两个或多个二进制数相乘：每行一个，或用空格、逗号、* 或 × 分隔，支持任意位数、负数和 0b 前缀；两个数相乘时可显示移位相加的竖式（部分积），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。适合学习二进制乘法、计算机组成原理和数字电路练习，数据在本地处理。Multiply two or more binary numbers. Put one per line or separate them with spaces, commas, * or ×. Any length, negative numbers and the 0b prefix work. For two numbers you can show the shift-and-add working with each partial product, and see the result in decimal and hex too, padded to a minimum width or grouped every 4 bits. Handy for learning binary multiplication, computer architecture and digital-logic exercises. Processed locally.
使用说明与常见问题How-to & FAQ
「二进制乘法计算器（多个二进制数相乘）」是什么？What is the Multiply Binary Numbers tool?
把两个或多个二进制数相乘：每行一个，或用空格、逗号、* 或 × 分隔，支持任意位数、负数和 0b 前缀；两个数相乘时可显示移位相加的竖式（部分积），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。适合学习二进制乘法、计算机组成原理和数字电路练习，数据在本地处理。Multiply two or more binary numbers. Put one per line or separate them with spaces, commas, * or ×. Any length, negative numbers and the 0b prefix work. For two numbers you can show the shift-and-add working with each partial product, and see the result in decimal and hex too, padded to a minimum width or grouped every 4 bits. Handy for learning binary multiplication, computer architecture and digital-logic exercises. Processed locally.
如何使用「二进制乘法计算器（多个二进制数相乘）」？How do I use the Multiply Binary Numbers tool?
在「二进制乘法计算器（多个二进制数相乘）」中，把内容粘贴或输入到上方输入框，按需设置「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「10*10*10」，得到「1000」。In the Multiply Binary Numbers: Paste or type into the input box, adjust "Minimum width (optional)"; the result appears below instantly — click "Copy result" to copy it. Example: "10*10*10" → "1000".
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.
二进制乘法的竖式怎么看？How do I read the working?
乘数从最低位开始，每一位如果是 1，就把被乘数抄下来并向左移一位；是 0 就写一行 0。最后把这些部分积相加就是结果。这正是计算机里“移位相加”乘法器的原理。Go through the multiplier from its lowest bit. For each 1, copy the multiplicand shifted one more place to the left; for each 0, write a row of zeros. Adding the partial products gives the result — exactly how a shift-and-add multiplier in a computer works.
可以用哪些乘号？Which multiplication signs can I use?
可以用 *、×、x 或 ·，也可以直接每行写一个数。勾选“数中间允许空格”时，* / × 等乘号仍会分开两个数（不会把 10*10 当成 1010）。负数前面加 - 号，结果按“负号 + 二进制”表示（不是补码）。Use *, ×, x or ·, or just put one number per line. With Allow spaces inside a number ticked, * / × still separate two values (so 10*10 is not read as 1010). Put - in front of a negative number; the result is shown with a sign (not as two's complement).
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，所以很长的二进制乘法也完全精确。All arithmetic uses BigInt (arbitrary-precision integers), not double-precision floats, so long binary multiplications stay exact.
输入和输出是什么样的？What does the input and output look like?
例如在「二进制乘法计算器（多个二进制数相乘）」中输入 101 ⏎ 11，输出为：1111（⏎ 表示换行）。For example, the Multiply Binary Numbers turns the input 101 ⏎ 11 into: 1111 (⏎ marks a line break).
有哪些选项可以调整？What options can I adjust?
「二进制乘法计算器（多个二进制数相乘）」的设置：「最少位数（可选）」可留空；可勾选：「显示竖式（部分积）」、「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 Multiply Binary Numbers — "Minimum width (optional)" optional; tick boxes: "Show the working (partial products)", "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.
「二进制乘法计算器（多个二进制数相乘）」免费吗？需要注册吗？Is the Multiply Binary Numbers free? Do I need an account?
「二进制乘法计算器（多个二进制数相乘）」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 Multiply 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.