---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- encoder
---

# threshold-binarytothermometer

Converts 3-bit binary to 7-bit thermometer code. A single-layer threshold circuit.

## Circuit

```
       b₂      b₁      b₀
        │       │       │
        │       │       │
    ┌───┴───┬───┴───┬───┴───┐
    │       │       │       │
    ▼       ▼       ▼       ▼
┌──────┐┌──────┐┌──────┐┌──────┐
│  y₀  ││  y₁  ││  y₂  ││ ...  │
│w:4,2,1│w:4,2,1│w:4,2,1│      │
│b: -1 ││b: -2 ││b: -3 ││      │
└──────┘└──────┘└──────┘└──────┘
    │       │       │       │
    ▼       ▼       ▼       ▼
   y₀      y₁      y₂  ... y₆
```

## Thermometer Code

Thermometer encoding represents value n as n consecutive ones:

| Value | Binary | Thermometer |
|-------|--------|-------------|
| 0 | 000 | 0000000 |
| 1 | 001 | 1000000 |
| 2 | 010 | 1100000 |
| 3 | 011 | 1110000 |
| 4 | 100 | 1111000 |
| 5 | 101 | 1111100 |
| 6 | 110 | 1111110 |
| 7 | 111 | 1111111 |

Like mercury rising in a thermometer - higher values fill more positions.

## Mechanism

Each output yᵢ fires when value > i:

```
yᵢ: (4·b₂ + 2·b₁ + 1·b₀) - (i+1) ≥ 0
```

The weights [4, 2, 1] compute the binary value. The bias sets the threshold.

| Output | Bias | Fires when |
|--------|------|------------|
| y₀ | -1 | value ≥ 1 |
| y₁ | -2 | value ≥ 2 |
| y₂ | -3 | value ≥ 3 |
| y₃ | -4 | value ≥ 4 |
| y₄ | -5 | value ≥ 5 |
| y₅ | -6 | value ≥ 6 |
| y₆ | -7 | value ≥ 7 |

## Why Thermometer?

Thermometer codes are used in:

- **DACs/ADCs**: Monotonic, glitch-free conversion
- **Flash ADCs**: Each comparator outputs one thermometer bit
- **Priority queues**: Natural ordering representation
- **Neural networks**: Unary encoding preserves magnitude relationships

## Single-Layer Elegance

This is one of the rare multi-output functions computable in a single layer. Each output is a simple threshold on the input value - no inter-neuron dependencies.

## Parameters

All neurons share the same weights, only biases differ:

| Component | Value |
|-----------|-------|
| Weights (all) | [4, 2, 1] |
| Biases | [-1, -2, -3, -4, -5, -6, -7] |

**Total: 7 neurons, 28 parameters, 1 layer**

## Usage

```python
from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def binary_to_therm(b2, b1, b0):
    inp = torch.tensor([float(b2), float(b1), float(b0)])
    return [int((inp * w[f'y{i}.weight']).sum() + w[f'y{i}.bias'] >= 0)
            for i in range(7)]

# Value 5 -> thermometer with 5 ones
therm = binary_to_therm(1, 0, 1)
print(therm)  # [1, 1, 1, 1, 1, 0, 0]
```

## Files

```
threshold-binarytothermometer/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```

## License

MIT