---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- floating-point
- normalization
---

# threshold-leading-one-detect

8-bit leading one detector. Finds the position of the highest-order 1 bit (MSB priority).

## Circuit

```
x[7:0] ──► LOD ──┬──► pos[2:0]  (position 0-7)
                 └──► valid     (1 if any bit set)
```

## Truth Table (examples)

| Input | Binary | Position | Valid |
|-------|--------|----------|-------|
| 0 | 00000000 | 0 | 0 |
| 1 | 00000001 | 0 | 1 |
| 2 | 00000010 | 1 | 1 |
| 128 | 10000000 | 7 | 1 |
| 255 | 11111111 | 7 | 1 |
| 170 | 10101010 | 7 | 1 |

## Algorithm

```
For each bit position i (7 down to 0):
  leader[i] = x[i] AND NOT(any bit j > i is set)

Position is binary encoding of which leader is active.
```

## Architecture

| Component | Count | Neurons |
|-----------|-------|---------|
| Higher-than OR | 8 | 8 |
| NOT higher | 8 | 8 |
| Leader AND | 8 | 8 |
| Position encode | 3 | 3 |
| Valid OR | 1 | 1 |

**Total: 28 neurons, 136 parameters, 3 layers**

## Applications

- **Floating-point normalization**: Find exponent adjustment
- **Priority encoding**: Highest-priority interrupt
- **Integer log₂**: Position = floor(log₂(x))
- **Bit manipulation**: Count leading zeros = 7 - position

## Usage

```python
from safetensors.torch import load_file

w = load_file('model.safetensors')

# For x = 0b00101100 (44):
# Leading one at position 5
# log₂(44) ≈ 5
```

## Relation to CLZ

Count Leading Zeros = 7 - position (when valid=1)
```
x = 0b00100000 → position=5 → CLZ=2
x = 0b10000000 → position=7 → CLZ=0
```

## Files

```
threshold-leading-one-detect/
├── model.safetensors
├── create_safetensors.py
├── config.json
└── README.md
```

## License

MIT