323 lines
10 KiB
Vue
323 lines
10 KiB
Vue
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<template>
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<div class="addition-rules">
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<div class="demo-header">
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<span class="title">从手算加法到逻辑门</span>
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<span class="subtitle">计算机如何只用 0 和 1 做数学题？看看这个规律</span>
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</div>
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<!-- 1. 十进制类比 -->
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<div class="section">
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<div class="section-title">第一步：回顾十进制的"进位"</div>
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<div class="decimal-analogy">
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<div class="math-column">
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<div class="math-row">
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<span class="digit carry-mark">1</span> <!-- 进位标记 -->
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</div>
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<div class="math-row">
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<span class="digit"></span>
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<span class="digit">7</span>
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</div>
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<div class="math-row">
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<span class="op">+</span>
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<span class="digit">5</span>
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</div>
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<div class="math-line"></div>
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<div class="math-row result-row">
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<span class="digit c-color">1</span>
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<span class="digit s-color">2</span>
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</div>
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</div>
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<div class="analogy-text">
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<p>
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因为 7 + 5 = 12，这个结果超出了个位能装下的最大数字 (9)。
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我们把 12 拆成"一个完整的 10"和"剩下的 2"：
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</p>
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<ul>
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<li>
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留在当前位置的那个 <span class="badge s-badge">2</span> 被<strong>写在个位</strong>上，这叫 <strong class="s-color">本位 (Sum)</strong>。
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</li>
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<li>
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"完整的 10"向十位<strong>进了一个 1</strong>，叫 <strong class="c-color">进位 (Carry)</strong>。
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</li>
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</ul>
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</div>
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</div>
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</div>
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<!-- 2. 二进制四种情况交互 -->
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<div class="section">
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<div class="section-title">第二步：二进制加法的 4 种情况（点点看）</div>
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<div class="binary-demo">
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<div class="binary-calc">
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<button class="bit-btn" :class="{ on: inputA }" @click="inputA = !inputA">{{ inputA ? '1' : '0' }}</button>
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<span class="op">+</span>
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<button class="bit-btn" :class="{ on: inputB }" @click="inputB = !inputB">{{ inputB ? '1' : '0' }}</button>
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<span class="op">=</span>
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<span class="res-box">
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<span class="res-bit carry-bit" :class="{ lit: carry }">{{ carry ? '1' : '0' }}</span>
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<span class="res-bit sum-bit" :class="{ lit: sum }">{{ sum ? '1' : '0' }}</span>
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</span>
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</div>
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<div class="binary-explain">
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<p v-if="!inputA && !inputB">
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0 + 0 = 0。<br>本位写 <strong>0</strong>，不进位。
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</p>
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<p v-if="(!inputA && inputB) || (inputA && !inputB)">
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{{ inputA ? '1' : '0' }} + {{ inputB ? '1' : '0' }} = 1。<br>本位写 <strong>1</strong>，不进位。
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</p>
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<p v-if="inputA && inputB">
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1 + 1 = 10。<br>
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二进制"满 2 就进 1"。所以本位写 <strong class="s-color">0</strong>，向左进位 <strong class="c-color">1</strong>。
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</p>
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</div>
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</div>
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</div>
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<!-- 3. 找出规律并对应到逻辑门 -->
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<div class="section mb-0">
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<div class="section-title">第三步：给规律起个名字（电路化）</div>
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<div class="rules-container">
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<!-- 所有的 4 种情况一览表 -->
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<div class="rules-table">
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<div class="rt-head">
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<span>A</span><span>B</span><span class="c-color">进位</span><span class="s-color">本位</span>
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</div>
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<div class="rt-row" :class="{ active: !inputA && !inputB }"><span>0</span><span>0</span><span>0</span><span>0</span></div>
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<div class="rt-row" :class="{ active: !inputA && inputB }"> <span>0</span><span>1</span><span>0</span><span>1</span></div>
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<div class="rt-row" :class="{ active: inputA && !inputB }"> <span>1</span><span>0</span><span>0</span><span>1</span></div>
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<div class="rt-row" :class="{ active: inputA && inputB }"> <span>1</span><span>1</span><span>1</span><span>0</span></div>
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</div>
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<div class="rules-text">
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<div class="rule-card sum-rule" :class="{ active: sum }">
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<div class="rc-title"><span class="badge s-badge">本位</span> 规律：</div>
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<div class="rc-desc">
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只有当输入是 (0,1) 或 (1,0) 时，本位才是 1。<br>
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<strong>总结：</strong>只有两个输入<strong>不同</strong>时才为 1。<br>
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<div class="rc-gate">这个规律在电路中叫 <strong>XOR (异或门)</strong></div>
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</div>
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</div>
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<div class="rule-card carry-rule" :class="{ active: carry }">
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<div class="rc-title"><span class="badge c-badge">进位</span> 规律：</div>
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<div class="rc-desc">
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只有当输入是 (1,1) 时，进位才是 1。<br>
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<strong>总结：</strong>只有两个输入<strong>都是 1</strong> 时才为 1。<br>
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<div class="rc-gate">这个规律在电路中叫 <strong>AND (与门)</strong></div>
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</div>
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</div>
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</div>
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</div>
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</div>
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</div>
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</template>
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<script setup>
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import { ref, computed } from 'vue'
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const inputA = ref(false)
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const inputB = ref(false)
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const sum = computed(() => inputA.value !== inputB.value)
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const carry = computed(() => inputA.value && inputB.value)
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</script>
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<style scoped>
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.addition-rules {
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border: 1px solid var(--vp-c-divider);
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border-radius: 10px;
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background: var(--vp-c-bg-soft);
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padding: 1.2rem;
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margin: 1.5rem 0;
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}
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.demo-header {
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margin-bottom: 1.2rem;
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}
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.title {
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display: block;
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font-size: 1rem;
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font-weight: bold;
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color: var(--vp-c-text-1);
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}
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.subtitle {
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font-size: 0.8rem;
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color: var(--vp-c-text-3);
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}
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.section {
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background: var(--vp-c-bg);
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border: 1px solid var(--vp-c-divider);
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border-radius: 8px;
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padding: 1rem;
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margin-bottom: 1rem;
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}
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.mb-0 { margin-bottom: 0; }
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.section-title {
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font-size: 0.85rem;
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font-weight: 600;
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color: var(--vp-c-brand-1);
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margin-bottom: 0.8rem;
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padding-bottom: 0.4rem;
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border-bottom: 1px dashed var(--vp-c-divider);
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}
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/* 颜色常量 */
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.s-color { color: #16a34a; font-weight: bold; }
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.c-color { color: #d97706; font-weight: bold; }
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.badge { padding: 0.15rem 0.4rem; border-radius: 4px; font-size: 0.75rem; font-family: monospace; }
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.s-badge { background: #dcfce7; color: #166534; }
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.c-badge { background: #fef3c7; color: #92400e; }
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/* 1. 十进制类比 */
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.decimal-analogy {
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display: flex;
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gap: 2rem;
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align-items: center;
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flex-wrap: wrap;
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}
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.math-column {
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display: inline-flex;
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flex-direction: column;
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align-items: flex-end;
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font-family: monospace;
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font-size: 1.5rem;
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background: var(--vp-c-bg-alt);
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padding: 1rem 1.5rem;
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border-radius: 6px;
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position: relative;
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}
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.math-row {
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display: flex;
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gap: 0.5rem;
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line-height: 1.2;
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}
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.digit { width: 1.2rem; text-align: center; }
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.op { font-weight: bold; color: var(--vp-c-text-3); margin-right: 0.2rem; }
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.math-line {
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width: 100%;
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height: 2px;
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background: var(--vp-c-text-2);
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margin: 0.2rem 0;
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}
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.carry-mark {
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color: #d97706;
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font-size: 0.8rem;
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line-height: 1;
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transform: translateY(10px);
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}
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.analogy-text {
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flex: 1;
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font-size: 0.8rem;
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color: var(--vp-c-text-2);
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line-height: 1.6;
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}
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.analogy-text ul { padding-left: 1.2rem; margin-top: 0.5rem; }
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/* 2. 二进制四种情况 */
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.binary-demo {
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display: flex;
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gap: 2rem;
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align-items: center;
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flex-wrap: wrap;
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}
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.binary-calc {
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display: flex;
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align-items: center;
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gap: 0.6rem;
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background: var(--vp-c-bg-alt);
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padding: 0.8rem 1.2rem;
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border-radius: 6px;
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}
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.bit-btn {
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width: 3rem; height: 3rem; font-size: 1.5rem; font-weight: bold; font-family: monospace;
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border-radius: 6px; background: var(--vp-c-bg); border: 2px solid var(--vp-c-divider);
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cursor: pointer; transition: all 0.2s;
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display: flex; align-items: center; justify-content: center;
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}
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.bit-btn.on { background: #dbeafe; color: #1d4ed8; border-color: #3b82f6; }
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.res-box { display: flex; gap: 0.2rem; margin-left: 0.5rem; }
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.res-bit {
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width: 3rem; height: 3rem; border-radius: 6px; border: 2px solid var(--vp-c-divider);
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background: var(--vp-c-bg); font-size: 1.5rem; font-weight: bold; font-family: monospace;
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display: flex; align-items: center; justify-content: center;
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color: var(--vp-c-text-3); transition: all 0.2s;
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}
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.carry-bit.lit { background: #fef3c7; color: #d97706; border-color: #d97706; }
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.sum-bit.lit { background: #dcfce7; color: #16a34a; border-color: #16a34a; }
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.binary-explain {
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flex: 1;
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background: var(--vp-c-bg-alt);
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padding: 0.8rem 1rem;
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border-radius: 6px;
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border-left: 3px solid #3b82f6;
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color: var(--vp-c-text-2);
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font-size: 0.85rem;
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line-height: 1.5;
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min-width: 200px;
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}
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.binary-explain p { margin: 0; }
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/* 3. 找出规律 */
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.rules-container {
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display: flex;
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gap: 1.5rem;
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flex-wrap: wrap;
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}
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.rules-table {
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flex: 0 0 auto;
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border: 1px solid var(--vp-c-divider);
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border-radius: 6px;
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overflow: hidden;
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font-family: monospace;
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font-size: 0.85rem;
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background: var(--vp-c-bg-alt);
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}
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.rt-head, .rt-row {
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display: grid;
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grid-template-columns: 2rem 2rem 3rem 3rem;
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text-align: center;
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padding: 0.4rem;
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border-bottom: 1px solid var(--vp-c-divider);
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}
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.rt-row:last-child { border-bottom: none; }
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.rt-head { font-weight: bold; font-family: system-ui; font-size: 0.75rem; background: var(--vp-c-bg); }
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.rt-row.active { background: #dbeafe; font-weight: bold; }
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.rules-text {
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flex: 1;
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display: flex;
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flex-direction: column;
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gap: 0.8rem;
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min-width: 250px;
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}
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.rule-card {
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border: 1px solid var(--vp-c-divider);
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border-radius: 8px;
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padding: 0.8rem;
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transition: all 0.2s;
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background: var(--vp-c-bg-alt);
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}
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.sum-rule.active { border-color: #16a34a; background: #f0fdf4; }
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.carry-rule.active { border-color: #d97706; background: #fffbeb; }
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.rc-title { font-size: 0.8rem; font-weight: bold; margin-bottom: 0.4rem; color: var(--vp-c-text-1); }
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.rc-desc { font-size: 0.75rem; color: var(--vp-c-text-2); line-height: 1.5; }
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.rc-gate {
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margin-top: 0.5rem;
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padding-top: 0.5rem;
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border-top: 1px dashed var(--vp-c-divider);
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color: var(--vp-c-brand-1);
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}
|
|||
|
|
|
|||
|
|
@media (max-width: 640px) {
|
|||
|
|
.decimal-analogy, .binary-demo, .rules-container { flex-direction: column; align-items: stretch; }
|
|||
|
|
.math-column, .rules-table { align-self: center; }
|
|||
|
|
}
|
|||
|
|
</style>
|