---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- bit-manipulation
---

# threshold-ctz4

4-bit count trailing zeros. Returns the number of consecutive zero bits starting from the LSB.

## Function

ctz4(x3, x2, x1, x0) -> count (0-4)

- CTZ = 0 if x0 = 1 (no trailing zeros)
- CTZ = 1 if x0 = 0, x1 = 1
- CTZ = 2 if x0 = x1 = 0, x2 = 1
- CTZ = 3 if x0 = x1 = x2 = 0, x3 = 1
- CTZ = 4 if all bits are zero

## Truth Table (selected rows)

| Input | CTZ | Output |
|-------|-----|--------|
| 0001 | 0 | 000 |
| 0010 | 1 | 001 |
| 0100 | 2 | 010 |
| 1000 | 3 | 011 |
| 0000 | 4 | 100 |
| 0110 | 1 | 001 |
| 1100 | 2 | 010 |

## Architecture

```
x3 x2 x1 x0
    │
    ▼
┌─────────────────────────────────┐
│ Layer 1: Prefix conditions      │
│ p0 = (x0=0)                     │
│ p01 = (x0=x1=0)                 │
│ p012 = (x0=x1=x2=0)             │
│ all_zero = (all=0)              │
└─────────────────────────────────┘
    │
    ▼
┌─────────────────────────────────┐
│ Layer 2: One-hot position       │
│ z1 = p0 AND x1                  │
│ z2 = p01 AND x2                 │
│ z3 = p012 AND x3                │
└─────────────────────────────────┘
    │
    ▼
┌─────────────────────────────────┐
│ Layer 3: Binary encoding        │
│ y2 = all_zero                   │
│ y1 = z2 OR z3                   │
│ y0 = z1 OR z3                   │
└─────────────────────────────────┘
    │
    ▼
  y2 y1 y0
```

## Parameters

| | |
|---|---|
| Inputs | 4 |
| Outputs | 3 |
| Neurons | 10 |
| Layers | 3 |
| Parameters | 37 |
| Magnitude | 30 |

## Usage

```python
from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

# ctz4(0,1,0,0) = 2 (binary 0100 has 2 trailing zeros)
# See model.py for full implementation
```

## Applications

- Finding the lowest set bit position
- Efficient division by powers of 2
- Bit manipulation in cryptography
- Hardware priority encoders

## License

MIT