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Tutoring abilities

Every smartphone, supercomputer, and video game console breaks complex decisions down into tiny electronic switches that only understand two states: **1 (HIGH voltage)** and **0 (LOW voltage)**.

In 1854, English mathematician George Boole introduced **Boolean algebra**—a system of formal logic where variables have only two values: true ($1$) or false ($0$).

We build physical circuits using **logic gates**, which are electronic devices that take one or more binary inputs and output a single binary result according to a rule.

A **truth table** lists every possible input combination alongside its exact output, giving us a complete map of how a gate behaves.

The **NOT gate** (or **inverter**) has only one input and simply flips the signal: a $0$ becomes a $1$, and a $1$ becomes a $0$.

The **AND gate** requires **both** input $A$ AND input $B$ to be $1$ to produce a $1$ output.

The **OR gate** produces a $1$ if **at least one** of its inputs ($A$ or $B$ or both) is $1$.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>OR Gate</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      user-select: none;
      -webkit-user-select: none;
    }

    body {
      background: #f8f9fa;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 16px;
      min-height: 100vh;
      gap: 16px;
    }

    .main-grid {
      display: grid;
      grid-template-columns: 1.2fr 0.8fr;
      gap: 16px;
      width: 100%;
      max-width: 540px;
      align-items: center;
    }

    @media (max-width: 460px) {
      .main-grid {
        grid-template-columns: 1fr;
        gap: 12px;
      }
    }

    /* Circuit Panel */
    .circuit-panel {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 16px 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      position: relative;
      box-shadow: 0 2px 6px rgba(0, 0, 0, 0.04);
    }

    .svg-container {
      width: 100%;
      max-width: 260px;
      height: auto;
      display: block;
    }

    /* Interactive Switch Buttons */
    .switch-btn {
      cursor: pointer;
      font-weight: 700;
      font-size: 14px;
      transition: fill 0.2s, stroke 0.2s;
    }

    .switch-bg {
      transition: fill 0.25s, stroke 0.25s;
    }

    .wire {
      transition: stroke 0.25s, stroke-width 0.25s;
    }

    .gate-body {
      transition: fill 0.25s, stroke 0.25s;
    }

    .output-indicator {
      transition: fill 0.25s, filter 0.25s;
    }

    /* Truth Table Panel */
    .table-panel {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 12px;
      box-shadow: 0 2px 6px rgba(0, 0, 0, 0.04);
    }

    table {
      width: 100%;
      border-collapse: separate;
      border-spacing: 0 4px;
      text-align: center;
      font-size: 14px;
    }

    th {
      color: #64748b;
      font-weight: 700;
      padding: 6px 8px;
      font-size: 13px;
    }

    .row-btn {
      cursor: pointer;
      transition: background 0.2s;
      border-radius: 6px;
    }

    .row-btn td {
      padding: 7px 8px;
      font-weight: 600;
    }

    .row-btn td:first-child {
      border-radius: 6px 0 0 6px;
    }

    .row-btn td:last-child {
      border-radius: 0 6px 6px 0;
    }

    .row-btn.active {
      background: #e0f2fe;
      color: #0284c7;
    }

    .row-btn:not(.active):hover {
      background: #f1f5f9;
    }

    .val-1 {
      color: #0284c7;
      font-weight: 700;
    }

    .val-0 {
      color: #94a3b8;
    }
  </style>
</head>
<body>

  <div class="main-grid">
    
    <div class="circuit-panel">
      <svg class="svg-container" viewBox="0 0 240 140">
        
        <line id="wireA" class="wire" x1="48" y1="42" x2="98" y2="42" stroke="#94a3b8" stroke-width="3" stroke-linecap="round"/>
        
        <line id="wireB" class="wire" x1="48" y1="98" x2="98" y2="98" stroke="#94a3b8" stroke-width="3" stroke-linecap="round"/>
        
        <line id="wireQ" class="wire" x1="168" y1="70" x2="204" y2="70" stroke="#94a3b8" stroke-width="3" stroke-linecap="round"/>

        
        <path id="gateShape" class="gate-body" 
              d="M 88 26 Q 112 70 88 114 Q 132 114 170 70 Q 132 26 88 26 Z" 
              fill="#ffffff" stroke="#1e2945" stroke-width="3" stroke-linejoin="round"/>

        
        <g id="btnA" class="switch-btn" transform="translate(10, 26)">
          <rect id="bgA" class="switch-bg" width="36" height="32" rx="6" fill="#f1f5f9" stroke="#cbd5e1" stroke-width="1.5"/>
          <text x="10" y="21" fill="#64748b" font-size="12" font-weight="700">A</text>
          <text id="txtA" x="24" y="21" fill="#64748b" font-size="14" font-weight="700">0</text>
        </g>

        
        <g id="btnB" class="switch-btn" transform="translate(10, 82)">
          <rect id="bgB" class="switch-bg" width="36" height="32" rx="6" fill="#f1f5f9" stroke="#cbd5e1" stroke-width="1.5"/>
          <text x="10" y="21" fill="#64748b" font-size="12" font-weight="700">B</text>
          <text id="txtB" x="24" y="21" fill="#64748b" font-size="14" font-weight="700">0</text>
        </g>

        
        <g transform="translate(204, 54)">
          <rect id="bgQ" class="output-indicator" width="28" height="32" rx="6" fill="#f1f5f9" stroke="#cbd5e1" stroke-width="1.5"/>
          <text id="txtQ" x="14" y="21" text-anchor="middle" fill="#64748b" font-size="14" font-weight="800">0</text>
        </g>
      </svg>
    </div>

    
    <div class="table-panel">
      <table>
        <thead>
          <tr>
            <th>A</th>
            <th>B</th>
            <th>Q</th>
          </tr>
        </thead>
        <tbody id="tableBody">
          <tr class="row-btn active" data-a="0" data-b="0">
            <td class="val-0">0</td>
            <td class="val-0">0</td>
            <td class="val-0">0</td>
          </tr>
          <tr class="row-btn" data-a="0" data-b="1">
            <td class="val-0">0</td>
            <td class="val-1">1</td>
            <td class="val-1">1</td>
          </tr>
          <tr class="row-btn" data-a="1" data-b="0">
            <td class="val-1">1</td>
            <td class="val-0">0</td>
            <td class="val-1">1</td>
          </tr>
          <tr class="row-btn" data-a="1" data-b="1">
            <td class="val-1">1</td>
            <td class="val-1">1</td>
            <td class="val-1">1</td>
          </tr>
        </tbody>
      </table>
    </div>
  </div>

  <script>
    let stateA = 0;
    let stateB = 0;

    const btnA = document.getElementById('btnA');
    const btnB = document.getElementById('btnB');
    const bgA = document.getElementById('bgA');
    const bgB = document.getElementById('bgB');
    const txtA = document.getElementById('txtA');
    const txtB = document.getElementById('txtB');
    const wireA = document.getElementById('wireA');
    const wireB = document.getElementById('wireB');
    const wireQ = document.getElementById('wireQ');
    const gateShape = document.getElementById('gateShape');
    const bgQ = document.getElementById('bgQ');
    const txtQ = document.getElementById('txtQ');
    const rows = document.querySelectorAll('.row-btn');

    const COLOR_HIGH = '#22b7ff';
    const COLOR_HIGH_BG = '#e0f2fe';
    const COLOR_LOW = '#94a3b8';
    const COLOR_LOW_BG = '#f1f5f9';

    function updateView() {
      const out = (stateA || stateB) ? 1 : 0;

      // Update Input A visual
      if (stateA === 1) {
        bgA.setAttribute('fill', COLOR_HIGH_BG);
        bgA.setAttribute('stroke', COLOR_HIGH);
        txtA.textContent = '1';
        txtA.setAttribute('fill', '#0284c7');
        wireA.setAttribute('stroke', COLOR_HIGH);
      } else {
        bgA.setAttribute('fill', COLOR_LOW_BG);
        bgA.setAttribute('stroke', '#cbd5e1');
        txtA.textContent = '0';
        txtA.setAttribute('fill', '#64748b');
        wireA.setAttribute('stroke', COLOR_LOW);
      }

      // Update Input B visual
      if (stateB === 1) {
        bgB.setAttribute('fill', COLOR_HIGH_BG);
        bgB.setAttribute('stroke', COLOR_HIGH);
        txtB.textContent = '1';
        txtB.setAttribute('fill', '#0284c7');
        wireB.setAttribute('stroke', COLOR_HIGH);
      } else {
        bgB.setAttribute('fill', COLOR_LOW_BG);
        bgB.setAttribute('stroke', '#cbd5e1');
        txtB.textContent = '0';
        txtB.setAttribute('fill', '#64748b');
        wireB.setAttribute('stroke', COLOR_LOW);
      }

      // Update Output visual
      if (out === 1) {
        wireQ.setAttribute('stroke', COLOR_HIGH);
        gateShape.setAttribute('fill', '#f0f9ff');
        gateShape.setAttribute('stroke', '#0284c7');
        bgQ.setAttribute('fill', COLOR_HIGH_BG);
        bgQ.setAttribute('stroke', COLOR_HIGH);
        txtQ.textContent = '1';
        txtQ.setAttribute('fill', '#0284c7');
      } else {
        wireQ.setAttribute('stroke', COLOR_LOW);
        gateShape.setAttribute('fill', '#ffffff');
        gateShape.setAttribute('stroke', '#1e2945');
        bgQ.setAttribute('fill', COLOR_LOW_BG);
        bgQ.setAttribute('stroke', '#cbd5e1');
        txtQ.textContent = '0';
        txtQ.setAttribute('fill', '#64748b');
      }

      // Highlight active table row
      rows.forEach(r => {
        const ra = parseInt(r.getAttribute('data-a'), 10);
        const rb = parseInt(r.getAttribute('data-b'), 10);
        if (ra === stateA && rb === stateB) {
          r.classList.add('active');
        } else {
          r.classList.remove('active');
        }
      });
    }

    btnA.addEventListener('click', () => {
      stateA = stateA === 1 ? 0 : 1;
      updateView();
    });

    btnB.addEventListener('click', () => {
      stateB = stateB === 1 ? 0 : 1;
      updateView();
    });

    rows.forEach(r => {
      r.addEventListener('click', () => {
        stateA = parseInt(r.getAttribute('data-a'), 10);
        stateB = parseInt(r.getAttribute('data-b'), 10);
        updateView();
      });
    });

    updateView();
  </script>
</body>
</html>

What if you need a condition where one person or the other can enter, but not both at the same time?

The **XOR gate** (Exclusive OR) outputs $1$ if the inputs are **different**, and outputs $0$ if both inputs are identical.

Its symbol looks just like an OR gate, but features an extra curved line along the input side, written algebraically as $Q = A \oplus B$.

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="aspect-ratio" content="4:3">
<title>Logic Gates & Truth Tables</title>
<style>
  * { box-sizing: border-box; margin: 0; padding: 0; }
  body {
    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
    background: transparent;
    color: #1e2945;
    display: flex;
    flex-direction: column;
    align-items: center;
    justify-content: center;
    padding: 10px;
    min-height: 100%;
    user-select: none;
  }

  .main-wrapper {
    width: 100%;
    max-width: 540px;
    display: flex;
    flex-direction: column;
    gap: 12px;
  }

  /* Gate Selector Tabs */
  .gate-tabs {
    display: flex;
    background: #f1f5f9;
    padding: 3px;
    border-radius: 10px;
    gap: 4px;
  }
  .gate-tab {
    flex: 1;
    text-align: center;
    padding: 8px 4px;
    font-size: 14px;
    font-weight: 600;
    border-radius: 8px;
    cursor: pointer;
    background: transparent;
    border: none;
    color: #64748b;
    transition: all 0.2s ease;
  }
  .gate-tab.active {
    background: #ffffff;
    color: #0284c7;
    box-shadow: 0 1px 3px rgba(0,0,0,0.08);
  }

  /* Workspace */
  .workspace {
    display: grid;
    grid-template-columns: 1.2fr 1fr;
    gap: 12px;
    align-items: stretch;
  }

  @media (max-width: 440px) {
    .workspace {
      grid-template-columns: 1fr;
    }
  }

  /* Schematic Card */
  .schematic-box {
    background: #ffffff;
    border: 1px solid #e2e8f0;
    border-radius: 12px;
    padding: 14px 10px;
    display: flex;
    flex-direction: column;
    justify-content: space-between;
    align-items: center;
    position: relative;
    box-shadow: 0 2px 4px rgba(0,0,0,0.02);
  }

  .svg-container {
    width: 100%;
    max-width: 220px;
    height: 110px;
  }

  svg {
    width: 100%;
    height: 100%;
    overflow: visible;
  }

  /* Switches area */
  .inputs-bar {
    display: flex;
    justify-content: space-around;
    width: 100%;
    padding-top: 6px;
    border-top: 1px solid #f1f5f9;
  }

  .toggle-btn {
    display: inline-flex;
    align-items: center;
    gap: 6px;
    padding: 6px 12px;
    border-radius: 8px;
    border: 1px solid #cbd5e1;
    background: #f8fafc;
    font-size: 13px;
    font-weight: 700;
    cursor: pointer;
    color: #475569;
    transition: all 0.15s ease;
  }
  .toggle-btn.on {
    background: #e0f2fe;
    border-color: #38bdf8;
    color: #0284c7;
  }
  .toggle-btn .state-badge {
    width: 18px;
    height: 18px;
    border-radius: 4px;
    display: inline-flex;
    align-items: center;
    justify-content: center;
    font-size: 11px;
    background: #cbd5e1;
    color: #ffffff;
  }
  .toggle-btn.on .state-badge {
    background: #0284c7;
  }

  /* Formula display */
  .formula-tag {
    font-size: 14px;
    font-weight: 700;
    color: #0369a1;
    background: #f0f9ff;
    padding: 3px 10px;
    border-radius: 20px;
    margin-bottom: 6px;
  }

  /* Truth Table */
  .table-box {
    background: #ffffff;
    border: 1px solid #e2e8f0;
    border-radius: 12px;
    padding: 10px;
    display: flex;
    flex-direction: column;
    justify-content: center;
    box-shadow: 0 2px 4px rgba(0,0,0,0.02);
  }

  table {
    width: 100%;
    border-collapse: separate;
    border-spacing: 0 4px;
    text-align: center;
    font-size: 13px;
  }

  th {
    padding: 4px 6px;
    color: #64748b;
    font-weight: 600;
    font-size: 12px;
    border-bottom: 1px solid #e2e8f0;
  }

  td {
    padding: 6px;
    font-weight: 600;
    color: #334155;
    background: #f8fafc;
    transition: background 0.15s ease, color 0.15s ease;
  }

  td:first-child { border-radius: 6px 0 0 6px; }
  td:last-child { border-radius: 0 6px 6px 0; }

  tr.active-row td {
    background: #0284c7;
    color: #ffffff;
    font-weight: 700;
  }

  tr.active-row td:last-child {
    background: #0369a1;
  }

  /* Output status pill */
  .output-badge {
    display: inline-flex;
    align-items: center;
    justify-content: center;
    min-width: 22px;
    height: 22px;
    border-radius: 50%;
    font-size: 12px;
    font-weight: 800;
  }
  .active-row .output-badge.val-1 {
    background: #38bdf8;
    color: #0c4a6e;
  }
  .active-row .output-badge.val-0 {
    background: #475569;
    color: #f8fafc;
  }
</style>
</head>
<body>

<div class="main-wrapper">
  
  <div class="gate-tabs">
    <button class="gate-tab active" data-gate="xor">XOR (⊕)</button>
    <button class="gate-tab" data-gate="or">OR (+)</button>
    <button class="gate-tab" data-gate="and">AND (·)</button>
  </div>

  <div class="workspace">
    
    <div class="schematic-box">
      <div class="formula-tag" id="formula">Q = A ⊕ B</div>

      <div class="svg-container">
        <svg viewBox="0 0 200 100">
          
          <line id="wireA" x1="10" y1="30" x2="65" y2="30" stroke="#94a3b8" stroke-width="4" stroke-linecap="round"/>
          <text id="lblA" x="22" y="22" font-size="11" font-weight="700" fill="#64748b">A</text>

          
          <line id="wireB" x1="10" y1="70" x2="65" y2="70" stroke="#94a3b8" stroke-width="4" stroke-linecap="round"/>
          <text id="lblB" x="22" y="88" font-size="11" font-weight="700" fill="#64748b">B</text>

          
          <line id="wireQ" x1="135" y1="50" x2="190" y2="50" stroke="#94a3b8" stroke-width="4" stroke-linecap="round"/>
          <circle id="bulb" cx="178" cy="50" r="7" fill="#cbd5e1" stroke="#94a3b8" stroke-width="2"/>
          <text id="lblQ" x="168" y="32" font-size="11" font-weight="700" fill="#64748b">Q</text>

          
          <g id="gatePaths" stroke="#0284c7" stroke-width="3.5" fill="#f0f9ff" stroke-linejoin="round" stroke-linecap="round">
            
            <path id="xorArc" d="M 54 18 Q 72 50 54 82" fill="none" stroke="#0284c7" stroke-width="3.5" />
            
            <path id="gateBody" d="M 64 18 Q 82 50 64 82 Q 106 82 135 50 Q 106 18 64 18 Z" />
          </g>
        </svg>
      </div>

      
      <div class="inputs-bar">
        <button class="toggle-btn" id="btnA">
          <span>A</span>
          <span class="state-badge" id="badgeA">0</span>
        </button>
        <button class="toggle-btn" id="btnB">
          <span>B</span>
          <span class="state-badge" id="badgeB">0</span>
        </button>
      </div>
    </div>

    
    <div class="table-box">
      <table>
        <thead>
          <tr>
            <th>A</th>
            <th>B</th>
            <th id="thQ">Q</th>
          </tr>
        </thead>
        <tbody id="tableBody">
          
        </tbody>
      </table>
    </div>
  </div>
</div>

<script>
  const GATES = {
    xor: {
      formula: 'Q = A ⊕ B',
      calc: (a, b) => a ^ b,
      arcVisible: true,
      bodyPath: 'M 64 18 Q 82 50 64 82 Q 106 82 135 50 Q 106 18 64 18 Z',
      wireAx2: 64,
      wireBx2: 64
    },
    or: {
      formula: 'Q = A + B',
      calc: (a, b) => a | b,
      arcVisible: false,
      bodyPath: 'M 60 18 Q 78 50 60 82 Q 106 82 135 50 Q 106 18 60 18 Z',
      wireAx2: 68,
      wireBx2: 68
    },
    and: {
      formula: 'Q = A · B',
      calc: (a, b) => a & b,
      arcVisible: false,
      bodyPath: 'M 60 18 L 95 18 A 32 32 0 0 1 95 82 L 60 82 Z',
      wireAx2: 60,
      wireBx2: 60
    }
  };

  let currentGate = 'xor';
  let inputA = 0;
  let inputB = 0;

  const btnA = document.getElementById('btnA');
  const btnB = document.getElementById('btnB');
  const badgeA = document.getElementById('badgeA');
  const badgeB = document.getElementById('badgeB');
  const wireA = document.getElementById('wireA');
  const wireB = document.getElementById('wireB');
  const wireQ = document.getElementById('wireQ');
  const bulb = document.getElementById('bulb');
  const formula = document.getElementById('formula');
  const xorArc = document.getElementById('xorArc');
  const gateBody = document.getElementById('gateBody');
  const tableBody = document.getElementById('tableBody');
  const tabs = document.querySelectorAll('.gate-tab');

  const COLOR_ON = '#0284c7';
  const COLOR_OFF = '#94a3b8';
  const BULB_ON = '#38bdf8';
  const BULB_OFF = '#cbd5e1';

  function update() {
    const gate = GATES[currentGate];
    const output = gate.calc(inputA, inputB);

    // Update Gate Formula & Shape
    formula.textContent = gate.formula;
    gateBody.setAttribute('d', gate.bodyPath);
    xorArc.style.display = gate.arcVisible ? 'block' : 'none';
    wireA.setAttribute('x2', gate.wireAx2);
    wireB.setAttribute('x2', gate.wireBx2);

    // Update Input UI
    badgeA.textContent = inputA;
    btnA.classList.toggle('on', inputA === 1);
    wireA.setAttribute('stroke', inputA === 1 ? COLOR_ON : COLOR_OFF);

    badgeB.textContent = inputB;
    btnB.classList.toggle('on', inputB === 1);
    wireB.setAttribute('stroke', inputB === 1 ? COLOR_ON : COLOR_OFF);

    // Update Output UI
    wireQ.setAttribute('stroke', output === 1 ? COLOR_ON : COLOR_OFF);
    bulb.setAttribute('fill', output === 1 ? BULB_ON : BULB_OFF);
    bulb.setAttribute('stroke', output === 1 ? COLOR_ON : COLOR_OFF);

    // Render Table
    const rows = [
      [0, 0],
      [0, 1],
      [1, 0],
      [1, 1]
    ];

    tableBody.innerHTML = rows.map(([a, b]) => {
      const q = gate.calc(a, b);
      const isActive = a === inputA && b === inputB;
      return `
        <tr class="${isActive ? 'active-row' : ''}" onclick="selectRow(${a}, ${b})">
          <td>${a}</td>
          <td>${b}</td>
          <td><span class="output-badge val-${q}">${q}</span></td>
        </tr>
      `;
    }).join('');
  }

  function selectRow(a, b) {
    inputA = a;
    inputB = b;
    update();
  }

  btnA.addEventListener('click', () => {
    inputA = inputA === 0 ? 1 : 0;
    update();
  });

  btnB.addEventListener('click', () => {
    inputB = inputB === 0 ? 1 : 0;
    update();
  });

  tabs.forEach(tab => {
    tab.addEventListener('click', () => {
      tabs.forEach(t => t.classList.remove('active'));
      tab.classList.add('active');
      currentGate = tab.dataset.gate;
      update();
    });
  });

  window.selectRow = selectRow;
  update();
</script>

</body>
</html>

Can we invert the results of standard AND and OR gates to save physical components on a silicon chip?

The **NAND gate** is simply an AND gate followed immediately by a NOT inverter: its output is $0$ **only** when all inputs are $1$.

The **NOR gate** is an OR gate followed by a NOT inverter: its output is $1$ **only** when all inputs are $0$.

In schematic symbols, this negation is represented by a small circular **inversion bubble** drawn at the gate's output tip.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Logic Gates and Truth Tables</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
      color: #1e2945;
      background: #f8f9fa;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 12px;
      user-select: none;
    }

    .nav-tabs {
      display: flex;
      flex-wrap: wrap;
      gap: 6px;
      justify-content: center;
      margin-bottom: 12px;
      width: 100%;
      max-width: 480px;
    }

    .tab-btn {
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      color: #1e2945;
      padding: 6px 12px;
      border-radius: 8px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      box-shadow: 0 1px 2px rgba(0,0,0,0.04);
      transition: all 0.2s ease;
    }

    .tab-btn.active {
      background: #22b7ff;
      border-color: #22b7ff;
      color: #ffffff;
      box-shadow: 0 2px 8px rgba(34, 183, 255, 0.35);
    }

    .workspace {
      display: grid;
      grid-template-columns: 1fr 120px;
      gap: 12px;
      width: 100%;
      max-width: 480px;
      align-items: center;
    }

    @media (max-width: 400px) {
      .workspace {
        grid-template-columns: 1fr;
      }
    }

    /* Circuit Canvas Box */
    .circuit-card {
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      border-radius: 12px;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 180px;
      position: relative;
    }

    .circuit-svg {
      width: 100%;
      max-width: 220px;
      height: 120px;
      overflow: visible;
    }

    .wire {
      stroke: #cbd5e1;
      stroke-width: 3;
      stroke-linecap: round;
      fill: none;
      transition: stroke 0.25s ease;
    }

    .wire.hi {
      stroke: #22b7ff;
    }

    .gate-body {
      fill: #ffffff;
      stroke: #1e2945;
      stroke-width: 2.5;
      stroke-linejoin: round;
    }

    .bubble {
      fill: #ffffff;
      stroke: #1e2945;
      stroke-width: 2;
    }

    /* Toggle Buttons */
    .io-btn {
      cursor: pointer;
      font-size: 12px;
      font-weight: 700;
      fill: #ffffff;
      transition: transform 0.15s ease;
    }

    .io-btn:hover {
      filter: brightness(0.95);
    }

    .io-pill {
      rx: 6;
      ry: 6;
      stroke-width: 1.5;
    }

    .io-pill.lo {
      fill: #f1f5f9;
      stroke: #94a3b8;
    }

    .io-pill.hi {
      fill: #22b7ff;
      stroke: #0284c7;
    }

    .io-text.lo {
      fill: #64748b;
    }

    .io-text.hi {
      fill: #ffffff;
    }

    /* Truth Table */
    .table-card {
      background: #ffffff;
      border: 1.5px solid #e2e8f0;
      border-radius: 12px;
      padding: 8px;
      display: flex;
      flex-direction: column;
      align-items: center;
    }

    .truth-table {
      width: 100%;
      border-collapse: collapse;
      font-size: 13px;
      text-align: center;
    }

    .truth-table th {
      padding: 4px;
      color: #64748b;
      font-weight: 600;
      border-bottom: 1.5px solid #e2e8f0;
    }

    .truth-table td {
      padding: 5px 4px;
      font-variant-numeric: tabular-nums;
      font-weight: 500;
      color: #334155;
    }

    .truth-table tr.active-row {
      background: #e0f2fe;
      font-weight: 700;
      color: #0284c7;
      border-radius: 6px;
    }

    .truth-table tr.active-row td {
      color: #0284c7;
    }
  </style>
</head>
<body>

  
  <div class="nav-tabs" id="gateTabs">
    <button class="tab-btn active" data-gate="AND">AND</button>
    <button class="tab-btn" data-gate="NAND">NAND</button>
    <button class="tab-btn" data-gate="OR">OR</button>
    <button class="tab-btn" data-gate="NOR">NOR</button>
    <button class="tab-btn" data-gate="XOR">XOR</button>
    <button class="tab-btn" data-gate="NOT">NOT</button>
  </div>

  <div class="workspace">
    
    <div class="circuit-card">
      <svg class="circuit-svg" viewBox="0 0 240 140" id="circuitSvg">
        
        <path id="wireA" class="wire" d="M 40,45 L 80,45" />
        <path id="wireB" class="wire" d="M 40,95 L 80,95" />

        
        <path id="wireOut" class="wire" d="M 160,70 L 195,70" />

        
        <g id="gateGraphic"></g>

        
        
        <g class="io-btn" id="btnA" transform="translate(10, 33)">
          <rect class="io-pill lo" width="34" height="24" />
          <text class="io-text lo" x="17" y="16" text-anchor="middle" font-size="12" font-weight="bold">A:0</text>
        </g>

        
        <g class="io-btn" id="btnB" transform="translate(10, 83)">
          <rect class="io-pill lo" width="34" height="24" />
          <text class="io-text lo" x="17" y="16" text-anchor="middle" font-size="12" font-weight="bold">B:0</text>
        </g>

        
        <g id="btnOut" transform="translate(195, 58)">
          <rect class="io-pill lo" id="outPill" width="34" height="24" />
          <text class="io-text lo" id="outText" x="17" y="16" text-anchor="middle" font-size="12" font-weight="bold">Q:0</text>
        </g>
      </svg>
    </div>

    
    <div class="table-card">
      <table class="truth-table" id="truthTable">
        
      </table>
    </div>
  </div>

  <script>
    const GATES = {
      AND: {
        inputs: 2,
        calc: (a, b) => a & b,
        svg: `<path class="gate-body" d="M 80,30 L 115,30 A 40,40 0 0 1 115,110 L 80,110 Z" />`
      },
      NAND: {
        inputs: 2,
        calc: (a, b) => (a & b) ? 0 : 1,
        svg: `
          <path class="gate-body" d="M 80,30 L 112,30 A 40,40 0 0 1 112,110 L 80,110 Z" />
          <circle class="bubble" cx="157" cy="70" r="5" />
        `
      },
      OR: {
        inputs: 2,
        calc: (a, b) => a | b,
        svg: `<path class="gate-body" d="M 75,30 Q 95,70 75,110 Q 120,110 155,70 Q 120,30 75,30 Z" />`
      },
      NOR: {
        inputs: 2,
        calc: (a, b) => (a | b) ? 0 : 1,
        svg: `
          <path class="gate-body" d="M 75,30 Q 95,70 75,110 Q 118,110 148,70 Q 118,30 75,30 Z" />
          <circle class="bubble" cx="154" cy="70" r="5" />
        `
      },
      XOR: {
        inputs: 2,
        calc: (a, b) => a ^ b,
        svg: `
          <path class="wire" d="M 70,30 Q 90,70 70,110" stroke-width="2.5" />
          <path class="gate-body" d="M 78,30 Q 98,70 78,110 Q 123,110 155,70 Q 123,30 78,30 Z" />
        `
      },
      NOT: {
        inputs: 1,
        calc: (a) => a ? 0 : 1,
        svg: `
          <path class="gate-body" d="M 85,35 L 142,70 L 85,105 Z" />
          <circle class="bubble" cx="148" cy="70" r="5" />
        `
      }
    };

    let currentGate = 'AND';
    let inputA = 0;
    let inputB = 0;

    function renderTable() {
      const gate = GATES[currentGate];
      const table = document.getElementById('truthTable');
      
      if (gate.inputs === 1) {
        let html = `<thead><tr><th>A</th><th>Q</th></tr></thead><tbody>`;
        [0, 1].forEach(a => {
          const q = gate.calc(a, 0);
          const active = (a === inputA);
          html += `<tr class="${active ? 'active-row' : ''}"><td>${a}</td><td>${q}</td></tr>`;
        });
        html += `</tbody>`;
        table.innerHTML = html;
      } else {
        let html = `<thead><tr><th>A</th><th>B</th><th>Q</th></tr></thead><tbody>`;
        [[0,0], [0,1], [1,0], [1,1]].forEach(([a, b]) => {
          const q = gate.calc(a, b);
          const active = (a === inputA && b === inputB);
          html += `<tr class="${active ? 'active-row' : ''}"><td>${a}</td><td>${b}</td><td>${q}</td></tr>`;
        });
        html += `</tbody>`;
        table.innerHTML = html;
      }
    }

    function updateCircuit() {
      const gate = GATES[currentGate];
      const isSingleInput = (gate.inputs === 1);

      // SVG structure
      document.getElementById('gateGraphic').innerHTML = gate.svg;

      // Adjust input wire & button visibility for NOT gate
      const btnB = document.getElementById('btnB');
      const wireB = document.getElementById('wireB');
      const wireA = document.getElementById('wireA');
      const btnA = document.getElementById('btnA');

      if (isSingleInput) {
        btnB.style.display = 'none';
        wireB.style.display = 'none';
        wireA.setAttribute('d', 'M 40,70 L 85,70');
        btnA.setAttribute('transform', 'translate(10, 58)');
      } else {
        btnB.style.display = 'block';
        wireB.style.display = 'block';
        wireA.setAttribute('d', 'M 40,45 L 80,45');
        btnA.setAttribute('transform', 'translate(10, 33)');
      }

      // Compute output
      const out = gate.calc(inputA, inputB);

      // Update Input A UI
      const pillA = btnA.querySelector('.io-pill');
      const textA = btnA.querySelector('.io-text');
      pillA.className.baseVal = `io-pill ${inputA ? 'hi' : 'lo'}`;
      textA.className.baseVal = `io-text ${inputA ? 'hi' : 'lo'}`;
      textA.textContent = `A:${inputA}`;
      wireA.className.baseVal = `wire ${inputA ? 'hi' : ''}`;

      // Update Input B UI
      if (!isSingleInput) {
        const pillB = btnB.querySelector('.io-pill');
        const textB = btnB.querySelector('.io-text');
        pillB.className.baseVal = `io-pill ${inputB ? 'hi' : 'lo'}`;
        textB.className.baseVal = `io-text ${inputB ? 'hi' : 'lo'}`;
        textB.textContent = `B:${inputB}`;
        wireB.className.baseVal = `wire ${inputB ? 'hi' : ''}`;
      }

      // Update Output UI
      const outPill = document.getElementById('outPill');
      const outText = document.getElementById('outText');
      const wireOut = document.getElementById('wireOut');
      outPill.className.baseVal = `io-pill ${out ? 'hi' : 'lo'}`;
      outText.className.baseVal = `io-text ${out ? 'hi' : 'lo'}`;
      outText.textContent = `Q:${out}`;
      wireOut.className.baseVal = `wire ${out ? 'hi' : ''}`;

      renderTable();
    }

    // Tab buttons
    document.querySelectorAll('.tab-btn').forEach(btn => {
      btn.addEventListener('click', () => {
        document.querySelectorAll('.tab-btn').forEach(b => b.classList.remove('active'));
        btn.classList.add('active');
        currentGate = btn.getAttribute('data-gate');
        updateCircuit();
      });
    });

    // Toggle Inputs
    document.getElementById('btnA').addEventListener('click', () => {
      inputA = inputA ? 0 : 1;
      updateCircuit();
    });

    document.getElementById('btnB').addEventListener('click', () => {
      inputB = inputB ? 0 : 1;
      updateCircuit();
    });

    // Initial render
    updateCircuit();
  </script>
</body>
</html>

A common mistake when reading schematics is confusing the flat-backed **AND/NAND** shape with the curved **OR/NOR** shape—always look at the input side line.

How do programmers express these gate operations directly in real software?

In JavaScript, we use logical operators like `&&` for AND, `||` for OR, and `!` for NOT to control execution flow.

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Logic Gates & Truth Tables</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; font-family: system-ui, -apple-system, sans-serif; }
    :root {
      --primary: #22b7ff;
      --primary-glow: rgba(34, 183, 255, 0.25);
      --text: #1e2945;
      --muted: #6b7280;
      --border: #e2e8f0;
      --bg: #f8fafc;
      --high: #22b7ff;
      --low: #94a3b8;
    }
    body {
      background: var(--bg);
      color: var(--text);
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }
    .nav-tabs {
      display: flex;
      flex-wrap: wrap;
      gap: 6px;
      justify-content: center;
      margin-bottom: 12px;
      width: 100%;
      max-width: 480px;
    }
    .tab-btn {
      background: #fff;
      border: 1px solid var(--border);
      color: var(--text);
      padding: 6px 12px;
      border-radius: 8px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      box-shadow: 0 1px 2px rgba(0,0,0,0.04);
      transition: all 0.2s ease;
    }
    .tab-btn.active {
      background: var(--primary);
      color: #fff;
      border-color: var(--primary);
      box-shadow: 0 2px 8px var(--primary-glow);
    }
    .main-stage {
      display: flex;
      flex-direction: row;
      align-items: center;
      justify-content: space-around;
      background: #fff;
      border-radius: 12px;
      padding: 14px 10px;
      width: 100%;
      max-width: 480px;
      gap: 12px;
      box-shadow: 0 2px 8px rgba(0,0,0,0.04);
    }
    @media (max-width: 420px) {
      .main-stage {
        flex-direction: column;
      }
    }
    .circuit-area {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
    }
    .inputs {
      display: flex;
      flex-direction: column;
      gap: 18px;
      align-items: center;
    }
    .toggle-btn {
      width: 42px;
      height: 38px;
      border-radius: 8px;
      border: 2px solid var(--border);
      background: #fff;
      font-size: 16px;
      font-weight: 700;
      color: var(--low);
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      transition: all 0.2s ease;
    }
    .toggle-btn.on {
      background: var(--primary);
      color: #fff;
      border-color: var(--primary);
      box-shadow: 0 0 10px var(--primary-glow);
    }
    .gate-svg {
      width: 130px;
      height: 100px;
    }
    .gate-body {
      fill: #fff;
      stroke: #1e2945;
      stroke-width: 2.5;
      stroke-linejoin: round;
    }
    .wire {
      stroke: var(--low);
      stroke-width: 2.5;
      stroke-linecap: round;
      fill: none;
      transition: stroke 0.2s ease;
    }
    .wire.on {
      stroke: var(--high);
    }
    .output-box {
      width: 44px;
      height: 44px;
      border-radius: 50%;
      border: 2px solid var(--low);
      background: #fff;
      color: var(--low);
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 18px;
      font-weight: 800;
      transition: all 0.2s ease;
    }
    .output-box.on {
      border-color: var(--primary);
      background: var(--primary);
      color: #fff;
      box-shadow: 0 0 14px var(--primary-glow);
    }
    .table-area {
      min-width: 130px;
    }
    table {
      width: 100%;
      border-collapse: collapse;
      font-size: 13px;
      text-align: center;
    }
    th {
      background: #f1f5f9;
      padding: 5px 8px;
      font-weight: 700;
      color: var(--text);
      border: 1px solid var(--border);
    }
    td {
      padding: 5px 8px;
      border: 1px solid var(--border);
      color: var(--muted);
      font-weight: 600;
      transition: background 0.2s, color 0.2s;
    }
    tr.active-row td {
      background: #e0f2fe;
      color: #0369a1;
      font-weight: 800;
    }
    tr.active-row td.out-cell {
      background: var(--primary);
      color: #fff;
    }
  </style>
</head>
<body>
  <div class="nav-tabs" id="gateTabs">
    <button class="tab-btn active" data-gate="AND">AND</button>
    <button class="tab-btn" data-gate="OR">OR</button>
    <button class="tab-btn" data-gate="NOT">NOT</button>
    <button class="tab-btn" data-gate="NAND">NAND</button>
    <button class="tab-btn" data-gate="NOR">NOR</button>
    <button class="tab-btn" data-gate="XOR">XOR</button>
  </div>

  <div class="main-stage">
    <div class="circuit-area">
      <div class="inputs">
        <button class="toggle-btn" id="btnA" aria-label="Input A">A: 0</button>
        <button class="toggle-btn" id="btnB" aria-label="Input B">B: 0</button>
      </div>

      <svg class="gate-svg" viewBox="0 0 130 100">
        
        <path id="wireA" class="wire" d="M 0 30 L 35 30" />
        <path id="wireB" class="wire" d="M 0 70 L 35 70" />
        
        
        <g id="gateGraphic"></g>

        
        <path id="wireOut" class="wire" d="M 95 50 L 130 50" />
      </svg>

      <div class="output-box" id="bulbOut">0</div>
    </div>

    <div class="table-area" id="tableContainer">
      
    </div>
  </div>

  <script>
    const gates = {
      AND: {
        inputs: 2,
        eval: (a, b) => a & b,
        svg: `<path class="gate-body" d="M 35 20 H 60 A 30 30 0 0 1 60 80 H 35 Z" />`
      },
      OR: {
        inputs: 2,
        eval: (a, b) => a | b,
        svg: `<path class="gate-body" d="M 32 20 Q 50 50 32 80 Q 65 78 88 50 Q 65 22 32 20 Z" />`
      },
      NOT: {
        inputs: 1,
        eval: (a) => a ? 0 : 1,
        svg: `<polygon class="gate-body" points="35,22 80,50 35,78" /><circle class="gate-body" cx="86" cy="50" r="5" />`
      },
      NAND: {
        inputs: 2,
        eval: (a, b) => (a & b) ? 0 : 1,
        svg: `<path class="gate-body" d="M 35 20 H 58 A 30 30 0 0 1 58 80 H 35 Z" /><circle class="gate-body" cx="92" cy="50" r="5" />`
      },
      NOR: {
        inputs: 2,
        eval: (a, b) => (a | b) ? 0 : 1,
        svg: `<path class="gate-body" d="M 30 20 Q 48 50 30 80 Q 63 78 82 50 Q 63 22 30 20 Z" /><circle class="gate-body" cx="88" cy="50" r="5" />`
      },
      XOR: {
        inputs: 2,
        eval: (a, b) => a ^ b,
        svg: `<path class="wire" d="M 26 20 Q 44 50 26 80" /><path class="gate-body" d="M 33 20 Q 51 50 33 80 Q 66 78 88 50 Q 66 22 33 20 Z" />`
      }
    };

    let currentGate = 'AND';
    let valA = 0;
    let valB = 0;

    const btnA = document.getElementById('btnA');
    const btnB = document.getElementById('btnB');
    const wireA = document.getElementById('wireA');
    const wireB = document.getElementById('wireB');
    const wireOut = document.getElementById('wireOut');
    const bulbOut = document.getElementById('bulbOut');
    const gateGraphic = document.getElementById('gateGraphic');
    const tableContainer = document.getElementById('tableContainer');
    const tabBtns = document.querySelectorAll('.tab-btn');

    function renderTable() {
      const g = gates[currentGate];
      let html = '<table><thead><tr>';
      if (g.inputs === 2) {
        html += '<th>A</th><th>B</th><th>Q</th></tr></thead><tbody>';
        const rows = [[0,0], [0,1], [1,0], [1,1]];
        rows.forEach(([a, b]) => {
          const q = g.eval(a, b);
          const isMatch = (a === valA && b === valB);
          html += `<tr class="${isMatch ? 'active-row' : ''}"><td>${a}</td><td>${b}</td><td class="${isMatch ? 'out-cell' : ''}">${q}</td></tr>`;
        });
      } else {
        html += '<th>A</th><th>Q</th></tr></thead><tbody>';
        [0, 1].forEach(a => {
          const q = g.eval(a);
          const isMatch = (a === valA);
          html += `<tr class="${isMatch ? 'active-row' : ''}"><td>${a}</td><td class="${isMatch ? 'out-cell' : ''}">${q}</td></tr>`;
        });
      }
      html += '</tbody></table>';
      tableContainer.innerHTML = html;
    }

    function update() {
      const g = gates[currentGate];
      gateGraphic.innerHTML = g.svg;

      if (g.inputs === 1) {
        btnB.style.visibility = 'hidden';
        wireB.style.display = 'none';
        wireA.setAttribute('d', 'M 0 50 L 35 50');
      } else {
        btnB.style.visibility = 'visible';
        wireB.style.display = 'block';
        wireA.setAttribute('d', 'M 0 30 L 35 30');
      }

      btnA.textContent = `A: ${valA}`;
      btnA.classList.toggle('on', valA === 1);
      wireA.classList.toggle('on', valA === 1);

      btnB.textContent = `B: ${valB}`;
      btnB.classList.toggle('on', valB === 1);
      wireB.classList.toggle('on', valB === 1);

      const out = g.inputs === 2 ? g.eval(valA, valB) : g.eval(valA);
      bulbOut.textContent = out;
      bulbOut.classList.toggle('on', out === 1);
      wireOut.classList.toggle('on', out === 1);

      renderTable();
    }

    btnA.addEventListener('click', () => {
      valA = valA === 0 ? 1 : 0;
      update();
    });

    btnB.addEventListener('click', () => {
      valB = valB === 0 ? 1 : 0;
      update();
    });

    tabBtns.forEach(tab => {
      tab.addEventListener('click', () => {
        tabBtns.forEach(t => t.classList.remove('active'));
        tab.classList.add('active');
        currentGate = tab.getAttribute('data-gate');
        update();
      });
    });

    update();
  </script>
</body>
</html>

As you practice drawing these six symbols, remember that NAND and NOR are known as **universal gates** because any digital circuit imaginable can be built using only one of them.

computer-science

Logic Gates and Truth Tables. Identify AND, OR, NOT, XOR, NAND, and NOR logic gates and draw their truth tables and symbols

Logic Gates and Truth Tables - A Level Computer Science

OCR / AQA A Level Computer Science: Logic Gates and Truth Tables (SLR15)

AQA and OCR A-Level Computer Science: Logic Gates & Truth Tables Revision Notes

When teaching logic gates at A2 Level, emphasize dual notation systems: standard ANSI/IEEE distinctive shapes (curved/pointed) vs. IEC rectangular shapes, as both may appear across UK exam boards (AQA, OCR, Cambridge 9618, Eduqas). Connect individual gate behaviors directly to universal gate properties (constructing any circuit using NAND/NOR alone) and encourage structured intermediate column generation in truth tables to avoid arithmetic and logic precedence errors.

Logic Gates and Truth Tables

The Fundamental Three: NOT, AND, OR

The Exclusive-OR (XOR) Gate