PUZZLE #10142: Logic Gate Circuit (diff 3)

logic-gate learn difficulty: 3/7 reason author: system unsolved

A digital logic circuit with 20 gates (2x AND, 6x NAND, 4x NOR, 8x OR). Simulate the gates forward from the given inputs. The output bits encode a 4-character word using 5-bit binary (A=00000 through Z=11001).

DATA

Difficulty	`3`
Word Length	`4`
Output Width	`20`
Encoding	`5-bit binary (A=00000, B=00001, ..., Z=11001)`
Gates	{'id': 'g0', 'type': 'OR', 'inputs': ['i0', 'i1'], 'output': 'o0'}, {'id': 'g1', 'type': 'OR', 'inputs': ['i2', 'i3'], 'output': 'o1'}, {'id': 'g2', 'type': 'NOR', 'inputs': ['i4', 'i5'], 'output': 'o2'}, {'id': 'g3', 'type': 'OR', 'inputs': ['i6', 'i7'], 'output': 'o3'}, {'id': 'g4', 'type': 'AND', 'inputs': ['i8', 'i9'], 'output': 'o4'}, {'id': 'g5', 'type': 'NAND', 'inputs': ['i10', 'i11'], 'output': 'o5'}, {'id': 'g6', 'type': 'NAND', 'inputs': ['i12', 'i13'], 'output': 'o6'}, {'id': 'g7', 'type': 'NOR', 'inputs': ['i14', 'i15'], 'output': 'o7'}, {'id': 'g8', 'type': 'NAND', 'inputs': ['i16', 'i17'], 'output': 'o8'}, {'id': 'g9', 'type': 'AND', 'inputs': ['i18', 'i19'], 'output': 'o9'}, {'id': 'g10', 'type': 'NOR', 'inputs': ['i20', 'i21'], 'output': 'o10'}, {'id': 'g11', 'type': 'NOR', 'inputs': ['i22', 'i23'], 'output': 'o11'}, {'id': 'g12', 'type': 'OR', 'inputs': ['i24', 'i25'], 'output': 'o12'}, {'id': 'g13', 'type': 'OR', 'inputs': ['i26', 'i27'], 'output': 'o13'}, {'id': 'g14', 'type': 'NAND', 'inputs': ['i28', 'i29'], 'output': 'o14'}, {'id': 'g15', 'type': 'NAND', 'inputs': ['i30', 'i31'], 'output': 'o15'}, {'id': 'g16', 'type': 'OR', 'inputs': ['i32', 'i33'], 'output': 'o16'}, {'id': 'g17', 'type': 'NAND', 'inputs': ['i34', 'i35'], 'output': 'o17'}, {'id': 'g18', 'type': 'OR', 'inputs': ['i36', 'i37'], 'output': 'o18'}, {'id': 'g19', 'type': 'OR', 'inputs': ['i38', 'i39'], 'output': 'o19'}
Inputs	{ "i0": 1, "i1": 0, "i10": 1, "i11": 1, "i12": 0, "i13": 1, "i14": 1, "i15": 1, "i16": 0, "i17": 0, "i18": 1, "i19": 1, "i2": 0, "i20": 1, "i21": 0, "i22": 1, "i23": 0, "i24": 1, "i25": 1, "i26": 0, "i27": 0, "i28": 1, "i29": 1, "i3": 0, "i30": 0, "i31": 1, "i32": 0, "i33": 0, "i34": 0, "i35": 1, "i36": 1, "i37": 1, "i38": 0, "i39": 0, "i4": 1, "i5": 0, "i6": 1, "i7": 1, "i8": 0, "i9": 0 }
Output Nodes	`o0, o1, o2, o3, o4, o5, o6, o7, o8, o9, o10, o11, o12, o13, o14, o15, o16, o17, o18, o19`
N Gates	`20`
N Inputs	`40`
Instructions	Digital logic circuit — simulate the gates forward. 1. Start with the given input values (bits). 2. For each gate in topological order: - Read its input values (from inputs or previous gate outputs) - Compute output based on gate type: BUF = input NOT = 1 - input AND = 1 if ALL inputs are 1, else 0 NAND = 0 if ALL inputs are 1, else 1 OR = 1 if ANY input is 1, else 0 NOR = 0 if ANY input is 1, else 1 XOR = 1 if odd number of 1s, else 0 XNOR = 1 if even number of 1s, else 0 3. After all gates are simulated, read the output nodes. 4. Group the output bits into 5-bit chunks. 5. Map each 5-bit value to a letter (0=A, 1=B, ..., 25=Z). 6. Concatenate to spell the hidden word.
Hint	`Logic circuit: 20 gates (2x AND, 6x NAND, 4x NOR, 8x OR), 40 inputs, 4 chars (20 output bits). Simulate forward, decode 5-bit binary.`
Answer Format	`5-bit binary string (e.g., "01010")`

{
  "type": "logic-gate",
  "difficulty": 3,
  "word_length": 4,
  "output_width": 20,
  "encoding": "5-bit binary (A=00000, B=00001, ..., Z=11001)",
  "gates": [
    {
      "id": "g0",
      "type": "OR",
      "inputs": [
        "i0",
        "i1"
      ],
      "output": "o0"
    },
    {
      "id": "g1",
      "type": "OR",
      "inputs": [
        "i2",
        "i3"
      ],
      "output": "o1"
    },
    {
      "id": "g2",
      "type": "NOR",
      "inputs": [
        "i4",
        "i5"
      ],
      "output": "o2"
    },
    {
      "id": "g3",
      "type": "OR",
      "inputs": [
        "i6",
        "i7"
      ],
      "output": "o3"
    },
    {
      "id": "g4",
      "type": "AND",
      "inputs": [
        "i8",
        "i9"
      ],
      "output": "o4"
    },
    {
      "id": "g5",
      "type": "NAND",
      "inputs": [
        "i10",
        "i11"
      ],
      "output": "o5"
    },
    {
      "id": "g6",
      "type": "NAND",
      "inputs": [
        "i12",
        "i13"
      ],
      "output": "o6"
    },
    {
      "id": "g7",
      "type": "NOR",
      "inputs": [
        "i14",
        "i15"
      ],
      "output": "o7"
    },
    {
      "id": "g8",
      "type": "NAND",
      "inputs": [
        "i16",
        "i17"
      ],
      "output": "o8"
    },
    {
      "id": "g9",
      "type": "AND",
      "inputs": [
        "i18",
        "i19"
      ],
      "output": "o9"
    },
    {
      "id": "g10",
      "type": "NOR",
      "inputs": [
        "i20",
        "i21"
      ],
      "output": "o10"
    },
    {
      "id": "g11",
      "type": "NOR",
      "inputs": [
        "i22",
        "i23"
      ],
      "output": "o11"
    },
    {
      "id": "g12",
      "type": "OR",
      "inputs": [
        "i24",
        "i25"
      ],
      "output": "o12"
    },
    {
      "id": "g13",
      "type": "OR",
      "inputs": [
        "i26",
        "i27"
      ],
      "output": "o13"
    },
    {
      "id": "g14",
      "type": "NAND",
      "inputs": [
        "i28",
        "i29"
      ],
      "output": "o14"
    },
    {
      "id": "g15",
      "type": "NAND",
      "inputs": [
        "i30",
        "i31"
      ],
      "output": "o15"
    },
    {
      "id": "g16",
      "type": "OR",
      "inputs": [
        "i32",
        "i33"
      ],
      "output": "o16"
    },
    {
      "id": "g17",
      "type": "NAND",
      "inputs": [
        "i34",
        "i35"
      ],
      "output": "o17"
    },
    {
      "id": "g18",
      "type": "OR",
      "inputs": [
        "i36",
        "i37"
      ],
      "output": "o18"
    },
    {
      "id": "g19",
      "type": "OR",
      "inputs": [
        "i38",
        "i39"
      ],
      "output": "o19"
    }
  ],
  "inputs": {
    "i0": 1,
    "i1": 0,
    "i10": 1,
    "i11": 1,
    "i12": 0,
    "i13": 1,
    "i14": 1,
    "i15": 1,
    "i16": 0,
    "i17": 0,
    "i18": 1,
    "i19": 1,
    "i2": 0,
    "i20": 1,
    "i21": 0,
    "i22": 1,
    "i23": 0,
    "i24": 1,
    "i25": 1,
    "i26": 0,
    "i27": 0,
    "i28": 1,
    "i29": 1,
    "i3": 0,
    "i30": 0,
    "i31": 1,
    "i32": 0,
    "i33": 0,
    "i34": 0,
    "i35": 1,
    "i36": 1,
    "i37": 1,
    "i38": 0,
    "i39": 0,
    "i4": 1,
    "i5": 0,
    "i6": 1,
    "i7": 1,
    "i8": 0,
    "i9": 0
  },
  "output_nodes": [
    "o0",
    "o1",
    "o2",
    "o3",
    "o4",
    "o5",
    "o6",
    "o7",
    "o8",
    "o9",
    "o10",
    "o11",
    "o12",
    "o13",
    "o14",
    "o15",
    "o16",
    "o17",
    "o18",
    "o19"
  ],
  "n_gates": 20,
  "n_inputs": 40,
  "instructions": "Digital logic circuit \u2014 simulate the gates forward.\n\n1. Start with the given input values (bits).\n2. For each gate in topological order:\n   - Read its input values (from inputs or previous gate outputs)\n   - Compute output based on gate type:\n     BUF = input\n     NOT = 1 - input\n     AND = 1 if ALL inputs are 1, else 0\n     NAND = 0 if ALL inputs are 1, else 1\n     OR = 1 if ANY input is 1, else 0\n     NOR = 0 if ANY input is 1, else 1\n     XOR = 1 if odd number of 1s, else 0\n     XNOR = 1 if even number of 1s, else 0\n3. After all gates are simulated, read the output nodes.\n4. Group the output bits into 5-bit chunks.\n5. Map each 5-bit value to a letter (0=A, 1=B, ..., 25=Z).\n6. Concatenate to spell the hidden word.",
  "hint": "Logic circuit: 20 gates (2x AND, 6x NAND, 4x NOR, 8x OR), 40 inputs, 4 chars (20 output bits). Simulate forward, decode 5-bit binary.",
  "answer_format": "5-bit binary string (e.g., \"01010\")"
}

author's note: Pool fill: logic-gate diff 3