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---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- comparison
---
# threshold-equal
8-bit equality comparator. Returns 1 if a = b, 0 otherwise.
## Circuit
```
a0 b0 a1 b1 a2 b2 a3 b3 a4 b4 a5 b5 a6 b6 a7 b7
│ │ │ │ │ │ │ │ │ │ │ │ │ │ │ │
└┬─┘ └┬─┘ └┬─┘ └┬─┘ └┬─┘ └┬─┘ └┬─┘ └┬─┘
▼ ▼ ▼ ▼ ▼ ▼ ▼ ▼
┌───┐ ┌───┐ ┌───┐ ┌───┐ ┌───┐ ┌───┐ ┌───┐ ┌───┐
│XOR│ │XOR│ │XOR│ │XOR│ │XOR│ │XOR│ │XOR│ │XOR│ L1-2
└───┘ └───┘ └───┘ └───┘ └───┘ └───┘ └───┘ └───┘
│ │ │ │ │ │ │ │
└───────┴───────┴───────┴───┬───┴───────┴───────┴───────┘
▼
┌─────────┐
│ NOR │ L3
│ w: -1×8 │
│ b: 0 │
└─────────┘
│
▼
(a = b)
```
## Mechanism
1. **XOR each bit pair**: XOR(a_i, b_i) = 1 if bits differ, 0 if same
2. **NOR all XORs**: Fires only when all XORs are 0 (all bits match)
The NOR gate acts as a "zero detector" - it fires when all its inputs are silent.
## XOR Structure (each)
```
a b
│ │
├─┬─┤
│ │ │
▼ │ ▼
┌────┐│┌────┐
│ OR │││NAND│
└────┘│└────┘
│ │ │
└─┼─┘
▼
┌──────┐
│ AND │
└──────┘
│
▼
XOR out
```
## Truth Table (sample)
| a | b | a = b |
|---|---|-------|
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 127 | 127 | 1 |
| 127 | 128 | 0 |
| 255 | 255 | 1 |
| 255 | 0 | 0 |
| 100 | 100 | 1 |
## Architecture
| Component | Neurons | Parameters |
|-----------|---------|------------|
| XOR × 8 | 24 | 72 |
| NOR | 1 | 9 |
| **Total** | **25** | **81** |
**Layers: 3** (XOR: 2, NOR: 1)
## Comparison Family
| Circuit | Condition | Implementation |
|---------|-----------|----------------|
| LessThan | a < b | borrow_out of (a - b) |
| **Equal** | a = b | NOR of all XOR bits |
| GreaterThan | a > b | LessThan(b, a) |
## Usage
```python
from safetensors.torch import load_file
w = load_file('model.safetensors')
def equal(a, b):
"""a, b: 8-bit lists [a0..a7] (LSB first)
Returns: 1 if a == b, 0 otherwise"""
# See model.py for full implementation
pass
# Example: 127 == 127?
a = [(127 >> i) & 1 for i in range(8)]
b = [(127 >> i) & 1 for i in range(8)]
result = equal(a, b) # Returns 1
```
## Files
```
threshold-equal/
├── model.safetensors
├── model.py
├── config.json
└── README.md
```
## License
MIT
|