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

# threshold-popcount4

4-bit population count. Counts the number of 1 bits in a 4-bit input.

## Function

popcount4(a, b, c, d) = binary count of 1 bits

Output [y2, y1, y0] is the 3-bit binary representation of the count (0-4).

## Truth Table

| a | b | c | d | count | y2 | y1 | y0 |
|---|---|---|---|-------|----|----|-----|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 |
| 0 | 0 | 1 | 1 | 2 | 0 | 1 | 0 |
| 0 | 1 | 1 | 1 | 3 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 4 | 1 | 0 | 0 |

## Architecture

```
         a   b   c   d
         |   |   |   |
    +----+---+---+---+----+
    |                     |
Layer 1:                  |
    y2 = (sum >= 4)       |
    ge2 = (sum >= 2)      |
    le3 = (sum <= 3)      |
    XOR(a,b) components   |
    XOR(c,d) components   |
    |                     |
Layer 2:                  |
    y1 = AND(ge2, le3)    |
    xor_ab = XOR(a,b)     |
    xor_cd = XOR(c,d)     |
    |                     |
Layer 3:                  |
    XOR(xor_ab, xor_cd)   |
    components            |
    |                     |
Layer 4:                  |
    y0 = XOR(xor_ab, xor_cd)
```

- **y2** (MSB): 1 when count = 4
- **y1**: 1 when count is 2 or 3
- **y0** (LSB): 1 when count is odd (parity = XOR4)

## Parameters

| | |
|---|---|
| Inputs | 4 |
| Outputs | 3 |
| Neurons | 13 |
| Layers | 4 |
| Parameters | 53 |
| Magnitude | 55 |

## Usage

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

w = load_file('model.safetensors')

# See model.py for full implementation
# popcount4(1, 0, 1, 1) returns [0, 1, 1] (count=3 = binary 011)
```

## License

MIT