Extract sign bit of 8-bit number, magnitude 2

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+---
+
+# threshold-signbit8
+
+Extract sign bit (MSB) of 8-bit number.
+
+## Function
+
+signbit8(a7..a0) = a7
+
+In 2's complement representation:
+- Output 0: non-negative (0 to 127)
+- Output 1: negative (-128 to -1)
+
+## Truth Table (selected)
+
+| unsigned | signed | signbit |
+|---------:|-------:|:-------:|
+| 0 | 0 | 0 |
+| 127 | +127 | 0 |
+| 128 | -128 | 1 |
+| 255 | -1 | 1 |
+
+## Architecture
+
+Single neuron extracting MSB:
+
+- Weights: [1, 0, 0, 0, 0, 0, 0, 0]
+- Bias: -1
+
+Fires when: a7 - 1 >= 0, i.e., a7 >= 1
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 8 |
+| Outputs | 1 |
+| Neurons | 1 |
+| Layers | 1 |
+| Parameters | 9 |
+| Magnitude | 2 |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+import torch
+
+w = load_file('model.safetensors')
+
+def signbit8(a7, a6, a5, a4, a3, a2, a1, a0):
+    inp = torch.tensor([float(a7), float(a6), float(a5), float(a4),
+                        float(a3), float(a2), float(a1), float(a0)])
+    return int((inp @ w['neuron.weight'].T + w['neuron.bias'] >= 0).item())
+
+print(signbit8(0, 1, 1, 1, 1, 1, 1, 1))  # 0 (value = +127)
+print(signbit8(1, 0, 0, 0, 0, 0, 0, 0))  # 1 (value = -128)
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-signbit8",
+  "description": "Extract sign bit (MSB) of 8-bit number",
+  "inputs": 8,
+  "outputs": 1,
+  "neurons": 1,
+  "layers": 1,
+  "parameters": 9
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+# Input order: a7..a0 (MSB to LSB)
+# Output sign bit (MSB = a7)
+weights = {
+    'neuron.weight': torch.tensor([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], dtype=torch.float32),
+    'neuron.bias': torch.tensor([-1.0], dtype=torch.float32)
+}
+save_file(weights, 'model.safetensors')
+
+def signbit8(bits):
+    inp = torch.tensor([float(b) for b in bits])
+    return int((inp @ weights['neuron.weight'].T + weights['neuron.bias'] >= 0).item())
+
+print("Verifying signbit8...")
+errors = 0
+for i in range(256):
+    bits = [(i >> (7-j)) & 1 for j in range(8)]
+    result = signbit8(bits)
+    expected = bits[0]  # sign bit is MSB (a7)
+    if result != expected:
+        errors += 1
+
+if errors == 0:
+    print("All 256 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 signbit8(a7, a6, a5, a4, a3, a2, a1, a0, weights):
+    """Returns sign bit (MSB) of 8-bit number. 1 = negative in 2's complement."""
+    inp = torch.tensor([float(a7), float(a6), float(a5), float(a4),
+                        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('signbit8 selected tests:')
+    for i in [0, 1, 127, 128, 255]:
+        bits = [(i >> (7-j)) & 1 for j in range(8)]
+        result = signbit8(*bits, w)
+        signed_val = i if i < 128 else i - 256
+        print(f'  {i:3d} ({i:08b}) signed={signed_val:+4d} -> sign={result}')