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license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- arithmetic
---
# threshold-fullsubtractor
Subtracts three 1-bit inputs (a, b, borrow_in), producing difference and borrow_out. The subtraction counterpart to the full adder.
## Circuit
```
a b
│ │
└───┬───┘
▼
┌─────────┐
│ HS1 │ First half subtractor
└─────────┘
│ │
d1 b1
│ \
│ bin \
└──┬──┘ \
▼ \
┌─────────┐ \
│ HS2 │ │
└─────────┘ │
│ │ │
diff b2 │
│ │
└──┬───┘
▼
┌──────┐
│ OR │
└──────┘
│
▼
bout
```
## Half Subtractor Detail
```
x y
│ │
├───┬───┤
│ │ │
▼ │ ▼
┌──────┐│┌──────┐ ┌───────┐
│ OR │││ NAND │ │ ¬x ∧ y│
│w:1,1 │││w:-1,-1│ │w:-1,1 │
│b: -1 │││b: +1 │ │b: -1 │
└──────┘│└──────┘ └───────┘
│ │ │ │
└───┼───┘ │
▼ │
┌──────┐ │
│ AND │ │
└──────┘ │
│ │
▼ ▼
diff borrow
```
## Truth Table
| a | b | bin | diff | bout |
|---|---|-----|------|------|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 |
Binary: a - b - bin = diff - (bout × 2)
## Composition
```
d1, b1 = HalfSubtractor(a, b)
diff, b2 = HalfSubtractor(d1, bin)
bout = OR(b1, b2)
```
A borrow propagates if either half subtractor produces one.
## Architecture
| Component | Neurons |
|-----------|---------|
| HS1 (a - b) | 4 |
| HS2 (d1 - bin) | 4 |
| OR (b1, b2) | 1 |
**Total: 9 neurons, 27 parameters, 4 layers**
## Contrast with Full Adder
| Circuit | Carry/Borrow | HS function |
|---------|--------------|-------------|
| FullAdder | cout = OR(c1, c2) | c = a AND b |
| FullSubtractor | bout = OR(b1, b2) | b = NOT(a) AND b |
The only structural difference: the borrow circuit uses NOT(a) AND b instead of AND.
## Usage
```python
from safetensors.torch import load_file
import torch
w = load_file('model.safetensors')
def full_subtractor(a, b, bin_in):
inp = torch.tensor([float(a), float(b)])
# HS1
hs1_l1 = (inp @ w['hs1.xor.layer1.weight'].T + w['hs1.xor.layer1.bias'] >= 0).float()
d1 = (hs1_l1 @ w['hs1.xor.layer2.weight'].T + w['hs1.xor.layer2.bias'] >= 0).float().item()
b1 = (inp @ w['hs1.borrow.weight'].T + w['hs1.borrow.bias'] >= 0).float().item()
# HS2
inp2 = torch.tensor([d1, float(bin_in)])
hs2_l1 = (inp2 @ w['hs2.xor.layer1.weight'].T + w['hs2.xor.layer1.bias'] >= 0).float()
diff = int((hs2_l1 @ w['hs2.xor.layer2.weight'].T + w['hs2.xor.layer2.bias'] >= 0).item())
b2 = (inp2 @ w['hs2.borrow.weight'].T + w['hs2.borrow.bias'] >= 0).float().item()
# Final borrow
bout = int((torch.tensor([b1, b2]) @ w['bout.weight'].T + w['bout.bias'] >= 0).item())
return diff, bout
```
## Files
```
threshold-fullsubtractor/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```
## License
MIT
|