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

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