---
license: mit
tags:
- pytorch
- safetensors
- threshold-logic
- neuromorphic
- arithmetic
- parallel-prefix
---

# threshold-kogge-stone

4-bit Kogge-Stone parallel prefix adder. Computes all carries in O(log n) depth using generate/propagate signals.

## Circuit

```
Inputs: A[3:0], B[3:0], Cin (9 inputs)
Outputs: S[3:0], Cout (5 outputs)

Level 0 - Generate/Propagate:
  G_i = A_i AND B_i
  P_i = A_i XOR B_i

Level 1-3 - Parallel Prefix:
  (G_high, P_high) o (G_low, P_low) = (G_high + P_high·G_low, P_high·P_low)

Final:
  C_i = G_i:0 + P_i:0·Cin
  S_i = P_i XOR C_{i-1}
```

## Kogge-Stone Structure (4-bit)

```
       G3,P3    G2,P2    G1,P1    G0,P0    Cin
         │        │        │        │       │
Level 1  ●────────●        ●────────●       │
         │        │        │        │       │
Level 2  ●────────┼────────●        │       │
         │        │        │        │       │
Level 3  ●────────┼────────┼────────●       │
         │        │        │        │       │
         ▼        ▼        ▼        ▼       │
       G3:0     G2:0     G1:0     G0      ──┘
         │        │        │        │
         ▼        ▼        ▼        ▼
       Cout      C2       C1       C0
                  │        │        │
                  ▼        ▼        ▼
                 S3       S2       S1       S0
```

## Advantage Over Ripple Carry

| Adder Type | Carry Depth | 4-bit | 64-bit |
|------------|-------------|-------|--------|
| Ripple Carry | O(n) | 4 | 64 |
| Kogge-Stone | O(log n) | 3 | 6 |

Kogge-Stone trades area for speed with maximum parallelism.

## Truth Table (Examples)

| A | B | Cin | S | Cout |
|---|---|-----|---|------|
| 0000 | 0000 | 0 | 0000 | 0 |
| 0101 | 0011 | 0 | 1000 | 0 |
| 1111 | 0001 | 0 | 0000 | 1 |
| 1111 | 1111 | 1 | 1111 | 1 |

## Parameters

| | |
|---|---|
| Inputs | 9 |
| Outputs | 5 |
| Neurons | 36 |
| Layers | 5 |
| Parameters | 132 |
| Magnitude | 56 |

## Usage

```python
from safetensors.torch import load_file

w = load_file('model.safetensors')

# All 512 input combinations verified correct
```

## Files

```
threshold-kogge-stone/
├── model.safetensors
├── create_safetensors.py
├── config.json
└── README.md
```

## License

MIT