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 ... y₆Thermometer 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) ≥ 0The 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 conversionFlash ADCs : Each comparator outputs one thermometer bitPriority queues : Natural ordering representationNeural 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
1 from safetensors . torch import load_file
2 import torch
3
4 w = load_file ( 'model.safetensors' )
5
6 def binary_to_therm ( b2 , b1 , b0 ) :
7 inp = torch . tensor ( [ float ( b2 ) , float ( b1 ) , float ( b0 ) ] )
8 return [ int ( ( inp * w [ f'y { i } .weight' ] ) . sum ( ) + w [ f'y { i } .bias' ] >= 0 )
9 for i in range ( 7 ) ]
10
11 # Value 5 -> thermometer with 5 ones
12 therm = binary_to_therm ( 1 , 0 , 1 )
13 print ( therm ) # [1, 1, 1, 1, 1, 0, 0]
Files
threshold-binarytothermometer/
├── model.safetensors
├── model.py
├── config.json
└── README.mdLicense
MIT
