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license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- arithmetic
---
# threshold-halfsubtractor
Subtracts two 1-bit inputs, producing difference and borrow. The subtraction counterpart to the half adder.
## Circuit
```
a b a b
│ │ │ │
├───┬───┤ └─┬─┘
│ │ │ │
▼ │ ▼ ▼
┌──────┐│┌──────┐ ┌───────┐
│ OR │││ NAND │ │ ¬a ∧ b│
│w:1,1 │││w:-1,-1│ │w:-1,1 │
│b: -1 │││b: +1 │ │b: -1 │
└──────┘│└──────┘ └───────┘
│ │ │ │
└───┼───┘ │
▼ │
┌──────┐ │
│ AND │ │
│w: 1,1│ │
│b: -2 │ │
└──────┘ │
│ │
▼ ▼
diff borrow
```
The diff output uses XOR (2 layers). The borrow output detects when we subtract 1 from 0.
## Truth Table
| a | b | diff | borrow |
|---|---|------|--------|
| 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 |
Binary: a - b = diff - (borrow × 2)
## Mechanism
**Diff (XOR):** Same as the half adder's sum. The difference bit is 1 when exactly one input is 1.
**Borrow:** Uses weights [-1, +1] with bias -1. This fires only when a=0 and b=1:
- a=0, b=0: -0 + 0 - 1 = -1 < 0 → no borrow
- a=0, b=1: -0 + 1 - 1 = 0 ≥ 0 → borrow
- a=1, b=0: -1 + 0 - 1 = -2 < 0 → no borrow
- a=1, b=1: -1 + 1 - 1 = -1 < 0 → no borrow
The borrow is NOT(a) AND b - we borrow when subtracting 1 from 0.
## Components
| Output | Function | Neurons | Layers |
|--------|----------|---------|--------|
| diff | XOR(a, b) | 3 | 2 |
| borrow | ¬a ∧ b | 1 | 1 |
**Total: 4 neurons, 12 parameters**
## Contrast with Half Adder
| Circuit | Output 2 | Function | Weights |
|---------|----------|----------|---------|
| HalfAdder | carry | a ∧ b | [1, 1], b=-2 |
| HalfSubtractor | borrow | ¬a ∧ b | [-1, 1], b=-1 |
The only difference: borrow has an inhibitory weight on a.
## Usage
```python
from safetensors.torch import load_file
import torch
w = load_file('model.safetensors')
def half_subtractor(a, b):
inp = torch.tensor([float(a), float(b)])
# XOR for diff
l1 = (inp @ w['xor.layer1.weight'].T + w['xor.layer1.bias'] >= 0).float()
diff = int((l1 @ w['xor.layer2.weight'].T + w['xor.layer2.bias'] >= 0).item())
# Borrow
borrow = int((inp @ w['borrow.weight'].T + w['borrow.bias'] >= 0).item())
return diff, borrow
```
## Files
```
threshold-halfsubtractor/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```
## License
MIT
|