0️⃣1️⃣ 二进制：电脑只认识0和10️⃣1️⃣ Binary: the computer only knows 0 and 1
地球的故事讲完啦，🌍蓝色星球向导把接力棒交给💻小电脑。可小电脑有点“笨”：它只认识0和1。这一片就看：只用两个数字，怎么数出全世界。The Earth stories are done, and the 🌍 blue-planet guide hands the baton to 💻 Little Computer. But Little Computer is a bit “simple”: it only knows 0 and 1. This leaf asks: with just two digits, how do you count the whole world?
第 1 步：电脑里只有开关Step 1: Only switches inside
先别急着数数——看看小电脑的脑子里有啥。Before counting, peek inside Little Computer's head.
小电脑脑子里全是小开关：灯亮叫“开”，记作1；灯灭叫“关”，记作0。没有第三种状态。所以数数只能用0和1，这就叫二进制：逢二进一。Little Computer's head is full of tiny switches: light on means “on”, written as 1; light off means “off”, written as 0. There is no third state. So counting uses only 0 and 1 — that is binary: every two rolls into one carry.
开关懂了，可我们平常用十进制，怎么翻成小电脑的话？Switches are clear — but we use decimal daily, so how do we translate it?
第 2 步：把十进制翻成01Step 2: Turn decimal into 0s and 1s
拿13举例：除以2记余数，一直除到0，再把余数倒着排，就是1101。小电脑看到四盏灯“亮亮灭亮”，就知道这是13。Take 13: divide by 2 and keep the remainder, repeat till 0, then read remainders backwards to get 1101. Little Computer sees four lamps “on-on-off-on” and knows it means 13.
能翻过去，还得翻回来——顺便问：为啥电脑不用十进制？Out is only half the trip — now back again, plus: why not decimal?
第 3 步：把01翻回来，为啥偏偏是2Step 3: Come back — and why 2, not 10
1101从右往左，位值是1、2、4、8：8+4+0+1=13，这叫按权展开。至于为啥是2：十种电压又贵又爱错，两种状态最结实，小电脑图个省心。Read 1101 right to left with place values 1, 2, 4, 8: 8+4+0+1 = 13, called place-value expansion. And why 2? Ten voltage levels cost more and glitch more; two states are tough — Little Computer likes simple and safe.
🎮 你来当翻译官（30 秒）🎮 Your turn: be the translator (30 seconds)
道理讲完了。先拖滑块，看数字和灯怎么联动；再闯下面4关，一半翻过去，一半翻回来。Theory done. First drag the slider and watch numbers and lamps move together; then clear 4 rounds — half out, half back.
一句话记住它：二进制=只用0和1数数，逢二进一；十进制除2取余倒着排翻过去，按权展开翻回来；电脑选2因为开关最可靠。Remember it in one line: binary counts with just 0 and 1 — every two carries; decimal goes out via divide-by-2 remainders read backwards, and comes back by place-value expansion; computers pick 2 because switches are toughest.
1位只有0/1两种状态，对应电路开/关One digit holds only 0 or 1 — a circuit on or off十进制→二进制：除2取余、倒着排（如13→1101）Decimal to binary: divide by 2, read remainders backwards (13 → 1101)二进制→十进制：按权展开（如1101=13）；选2因硬件简单可靠Binary to decimal: expand by place value (1101 = 13); 2 wins for simple, reliable hardware
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
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