PUZZLE #3085: Logic Gate Circuit (diff 1)

logic-gate learn difficulty: 1/7 reason author: system unsolved

A digital logic circuit with 15 gates (15x NOT). Simulate the gates forward from the given inputs. The output bits encode a 3-character word using 5-bit binary (A=00000 through Z=11001).

DATA

Difficulty	`1`
Word Length	`3`
Output Width	`15`
Encoding	`5-bit binary (A=00000, B=00001, ..., Z=11001)`
Gates	{'id': 'g0', 'type': 'NOT', 'inputs': ['i0'], 'output': 'o0'}, {'id': 'g1', 'type': 'NOT', 'inputs': ['i1'], 'output': 'o1'}, {'id': 'g2', 'type': 'NOT', 'inputs': ['i2'], 'output': 'o2'}, {'id': 'g3', 'type': 'NOT', 'inputs': ['i3'], 'output': 'o3'}, {'id': 'g4', 'type': 'NOT', 'inputs': ['i4'], 'output': 'o4'}, {'id': 'g5', 'type': 'NOT', 'inputs': ['i5'], 'output': 'o5'}, {'id': 'g6', 'type': 'NOT', 'inputs': ['i6'], 'output': 'o6'}, {'id': 'g7', 'type': 'NOT', 'inputs': ['i7'], 'output': 'o7'}, {'id': 'g8', 'type': 'NOT', 'inputs': ['i8'], 'output': 'o8'}, {'id': 'g9', 'type': 'NOT', 'inputs': ['i9'], 'output': 'o9'}, {'id': 'g10', 'type': 'NOT', 'inputs': ['i10'], 'output': 'o10'}, {'id': 'g11', 'type': 'NOT', 'inputs': ['i11'], 'output': 'o11'}, {'id': 'g12', 'type': 'NOT', 'inputs': ['i12'], 'output': 'o12'}, {'id': 'g13', 'type': 'NOT', 'inputs': ['i13'], 'output': 'o13'}, {'id': 'g14', 'type': 'NOT', 'inputs': ['i14'], 'output': 'o14'}
Inputs	{ "i0": 1, "i1": 0, "i10": 0, "i11": 0, "i12": 1, "i13": 1, "i14": 1, "i2": 1, "i3": 0, "i4": 0, "i5": 1, "i6": 1, "i7": 1, "i8": 1, "i9": 1 }
Output Nodes	`o0, o1, o2, o3, o4, o5, o6, o7, o8, o9, o10, o11, o12, o13, o14`
N Gates	`15`
N Inputs	`15`
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: 15 gates (15x NOT), 15 inputs, 3 chars (15 output bits). Simulate forward, decode 5-bit binary.`
Answer Format	`5-bit binary string (e.g., "01010")`

{
  "type": "logic-gate",
  "difficulty": 1,
  "word_length": 3,
  "output_width": 15,
  "encoding": "5-bit binary (A=00000, B=00001, ..., Z=11001)",
  "gates": [
    {
      "id": "g0",
      "type": "NOT",
      "inputs": [
        "i0"
      ],
      "output": "o0"
    },
    {
      "id": "g1",
      "type": "NOT",
      "inputs": [
        "i1"
      ],
      "output": "o1"
    },
    {
      "id": "g2",
      "type": "NOT",
      "inputs": [
        "i2"
      ],
      "output": "o2"
    },
    {
      "id": "g3",
      "type": "NOT",
      "inputs": [
        "i3"
      ],
      "output": "o3"
    },
    {
      "id": "g4",
      "type": "NOT",
      "inputs": [
        "i4"
      ],
      "output": "o4"
    },
    {
      "id": "g5",
      "type": "NOT",
      "inputs": [
        "i5"
      ],
      "output": "o5"
    },
    {
      "id": "g6",
      "type": "NOT",
      "inputs": [
        "i6"
      ],
      "output": "o6"
    },
    {
      "id": "g7",
      "type": "NOT",
      "inputs": [
        "i7"
      ],
      "output": "o7"
    },
    {
      "id": "g8",
      "type": "NOT",
      "inputs": [
        "i8"
      ],
      "output": "o8"
    },
    {
      "id": "g9",
      "type": "NOT",
      "inputs": [
        "i9"
      ],
      "output": "o9"
    },
    {
      "id": "g10",
      "type": "NOT",
      "inputs": [
        "i10"
      ],
      "output": "o10"
    },
    {
      "id": "g11",
      "type": "NOT",
      "inputs": [
        "i11"
      ],
      "output": "o11"
    },
    {
      "id": "g12",
      "type": "NOT",
      "inputs": [
        "i12"
      ],
      "output": "o12"
    },
    {
      "id": "g13",
      "type": "NOT",
      "inputs": [
        "i13"
      ],
      "output": "o13"
    },
    {
      "id": "g14",
      "type": "NOT",
      "inputs": [
        "i14"
      ],
      "output": "o14"
    }
  ],
  "inputs": {
    "i0": 1,
    "i1": 0,
    "i10": 0,
    "i11": 0,
    "i12": 1,
    "i13": 1,
    "i14": 1,
    "i2": 1,
    "i3": 0,
    "i4": 0,
    "i5": 1,
    "i6": 1,
    "i7": 1,
    "i8": 1,
    "i9": 1
  },
  "output_nodes": [
    "o0",
    "o1",
    "o2",
    "o3",
    "o4",
    "o5",
    "o6",
    "o7",
    "o8",
    "o9",
    "o10",
    "o11",
    "o12",
    "o13",
    "o14"
  ],
  "n_gates": 15,
  "n_inputs": 15,
  "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: 15 gates (15x NOT), 15 inputs, 3 chars (15 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 1