File size: 4,291 Bytes
6a0af35 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 | ---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- parity
- error-detection
---
# threshold-parity7
7-bit parity function. Outputs 1 if an odd number of inputs are high. Essential for error detection in 7-bit data words.
## Circuit
```
x0 x1 x2 x3 x4 x5 x6
│ │ │ │ │ │ │
└─┬─┘ └─┬─┘ └─┬─┘ │
│ │ │ │
▼ ▼ ▼ │
┌─────┐ ┌─────┐ ┌─────┐ │
│XOR01│ │XOR23│ │XOR45│ │ Level 1
└─────┘ └─────┘ └─────┘ │
│ │ │ │
└────┬────┘ └───┬───┘
│ │
▼ ▼
┌───────┐ ┌───────┐
│XOR0123│ │XOR456 │ Level 2
└───────┘ └───────┘
│ │
└────────┬─────────┘
│
▼
┌─────────┐
│XOR_final│ Level 3
└─────────┘
│
▼
parity
```
## Function
```
parity7(x0..x6) = x0 XOR x1 XOR x2 XOR x3 XOR x4 XOR x5 XOR x6
```
Returns 1 when the Hamming weight is odd (1, 3, 5, or 7).
## Truth Table (by Hamming Weight)
| HW | Example Input | Parity |
|:--:|---------------|:------:|
| 0 | 0000000 | 0 |
| 1 | 0000001 | 1 |
| 2 | 0000011 | 0 |
| 3 | 0000111 | 1 |
| 4 | 0001111 | 0 |
| 5 | 0011111 | 1 |
| 6 | 0111111 | 0 |
| 7 | 1111111 | 1 |
## Mechanism
**XOR Implementation (3 neurons per gate):**
Each XOR is built from OR, NAND, and AND gates:
```
XOR(a, b) = AND(OR(a,b), NAND(a,b))
```
| Gate | Weights | Bias | Fires when |
|------|---------|------|------------|
| OR | [1, 1] | -1 | a + b >= 1 |
| NAND | [-1, -1] | +1 | a + b <= 1 |
| AND | [1, 1] | -2 | both inputs = 1 |
**Tree Structure (6 XOR gates):**
| Level | Gates | Computes |
|-------|-------|----------|
| 1 | XOR01, XOR23, XOR45 | Pairs of inputs |
| 2 | XOR0123, XOR456 | XOR(XOR01,XOR23), XOR(XOR45,x6) |
| 3 | XOR_final | XOR(XOR0123, XOR456) |
## Architecture
| Component | Function | Neurons |
|-----------|----------|---------|
| xor_01 | x0 XOR x1 | 3 |
| xor_23 | x2 XOR x3 | 3 |
| xor_45 | x4 XOR x5 | 3 |
| xor_0123 | xor01 XOR xor23 | 3 |
| xor_456 | xor45 XOR x6 | 3 |
| xor_final | xor0123 XOR xor456 | 3 |
**Total: 18 neurons, 6 XOR gates**
## Parameters
| | |
|---|---|
| Inputs | 7 |
| Outputs | 1 |
| Neurons | 18 |
| Layers | 6 |
| Parameters | 54 |
| Magnitude | 60 |
## Usage
```python
from safetensors.torch import load_file
import torch
w = load_file('model.safetensors')
def xor2(a, b, prefix):
or_out = int(a * w[f'{prefix}.or.weight'][0] + b * w[f'{prefix}.or.weight'][1] + w[f'{prefix}.or.bias'] >= 0)
nand_out = int(a * w[f'{prefix}.nand.weight'][0] + b * w[f'{prefix}.nand.weight'][1] + w[f'{prefix}.nand.bias'] >= 0)
return int(or_out * w[f'{prefix}.and.weight'][0] + nand_out * w[f'{prefix}.and.weight'][1] + w[f'{prefix}.and.bias'] >= 0)
def parity7(x0, x1, x2, x3, x4, x5, x6):
xor01 = xor2(x0, x1, 'xor_01')
xor23 = xor2(x2, x3, 'xor_23')
xor45 = xor2(x4, x5, 'xor_45')
xor0123 = xor2(xor01, xor23, 'xor_0123')
xor456 = xor2(xor45, x6, 'xor_456')
return xor2(xor0123, xor456, 'xor_final')
# Examples
print(parity7(1, 0, 1, 0, 1, 0, 0)) # 1 (odd: 3 ones)
print(parity7(1, 1, 1, 1, 1, 1, 1)) # 1 (odd: 7 ones)
print(parity7(1, 1, 0, 0, 0, 0, 0)) # 0 (even: 2 ones)
```
## Applications
- Hamming(7,4) code parity bit
- 7-bit ASCII parity checking
- Memory word error detection
- Bus parity generation
## Files
```
threshold-parity7/
├── model.safetensors
├── model.py
├── create_safetensors.py
├── config.json
└── README.md
```
## License
MIT
|