Extract sign bit of 4-bit number, magnitude 2

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+---
+
+# threshold-signbit4
+
+Extract sign bit (MSB) of 4-bit number.
+
+## Function
+
+signbit4(a3, a2, a1, a0) = a3
+
+In 2's complement representation:
+- Output 0: non-negative (0 to 7)
+- Output 1: negative (-8 to -1)
+
+## Truth Table
+
+| a3 | a2 | a1 | a0 | unsigned | signed | signbit |
+|----|----|----|----|---------:|-------:|:-------:|
+| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
+| 0 | 1 | 1 | 1 | 7 | +7 | 0 |
+| 1 | 0 | 0 | 0 | 8 | -8 | 1 |
+| 1 | 1 | 1 | 1 | 15 | -1 | 1 |
+
+## Architecture
+
+Single neuron extracting MSB:
+
+- Weights: [1, 0, 0, 0]
+- Bias: -1
+
+Fires when: a3 - 1 >= 0, i.e., a3 >= 1
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 4 |
+| Outputs | 1 |
+| Neurons | 1 |
+| Layers | 1 |
+| Parameters | 5 |
+| Magnitude | 2 |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def signbit4(a3, a2, a1, a0):
+    inp = torch.tensor([float(a3), float(a2), float(a1), float(a0)])
+    return int((inp @ w['neuron.weight'].T + w['neuron.bias'] >= 0).item())
+
+print(signbit4(0, 1, 1, 1))  # 0 (value = +7)
+print(signbit4(1, 0, 0, 0))  # 1 (value = -8)
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-signbit4",
+  "description": "Extract sign bit (MSB) of 4-bit number",
+  "inputs": 4,
+  "outputs": 1,
+  "neurons": 1,
+  "layers": 1,
+  "parameters": 5
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+# Input order: a3, a2, a1, a0 (MSB to LSB)
+# Output sign bit (MSB = a3)
+# In 2's complement, a3=1 means negative
+weights = {
+    'neuron.weight': torch.tensor([[1.0, 0.0, 0.0, 0.0]], dtype=torch.float32),
+    'neuron.bias': torch.tensor([-1.0], dtype=torch.float32)
+}
+save_file(weights, 'model.safetensors')
+
+def signbit4(a3, a2, a1, a0):
+    inp = torch.tensor([float(a3), float(a2), float(a1), float(a0)])
+    return int((inp @ weights['neuron.weight'].T + weights['neuron.bias'] >= 0).item())
+
+print("Verifying signbit4...")
+errors = 0
+for i in range(16):
+    a3, a2, a1, a0 = (i >> 3) & 1, (i >> 2) & 1, (i >> 1) & 1, i & 1
+    result = signbit4(a3, a2, a1, a0)
+    expected = a3  # sign bit is MSB
+    if result != expected:
+        errors += 1
+        print(f"ERROR: {a3}{a2}{a1}{a0} -> {result}, expected {expected}")
+
+if errors == 0:
+    print("All 16 test cases passed!")
+print(f"Magnitude: {sum(t.abs().sum().item() for t in weights.values()):.0f}")

model.py

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+import torch
+from safetensors.torch import load_file
+
+def load_model(path='model.safetensors'):
+    return load_file(path)
+
+def signbit4(a3, a2, a1, a0, weights):
+    """Returns sign bit (MSB) of 4-bit number. 1 = negative in 2's complement."""
+    inp = torch.tensor([float(a3), float(a2), float(a1), float(a0)])
+    return int((inp @ weights['neuron.weight'].T + weights['neuron.bias'] >= 0).item())
+
+if __name__ == '__main__':
+    w = load_model()
+    print('signbit4 truth table:')
+    for i in range(16):
+        a3, a2, a1, a0 = (i >> 3) & 1, (i >> 2) & 1, (i >> 1) & 1, i & 1
+        result = signbit4(a3, a2, a1, a0, w)
+        signed_val = i if i < 8 else i - 16
+        print(f'  {a3}{a2}{a1}{a0} (unsigned={i:2d}, signed={signed_val:+3d}) -> sign={result}')