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

# threshold-twos-complement

4-bit two's complement negation circuit. Computes -A for signed integers.

## Circuit

```
A[3:0] ──► Negate ──┬──► N[3:0]    (-A)
                    └──► overflow  (when A = -8)
```

## Algorithm

```
-A = ~A + 1

1. Invert all bits
2. Add 1
```

## Truth Table

| A (unsigned) | A (signed) | N (signed) | Overflow |
|--------------|------------|------------|----------|
| 0000 (0) | +0 | +0 | 0 |
| 0001 (1) | +1 | -1 | 0 |
| 0111 (7) | +7 | -7 | 0 |
| 1000 (8) | -8 | -8 | 1 |
| 1111 (15) | -1 | +1 | 0 |

## Overflow

The value -8 (1000) cannot be negated in 4-bit two's complement:
- Range: -8 to +7
- -(-8) = +8, which exceeds +7
- Result wraps to -8, overflow flag set

## Architecture

| Component | Count | Neurons |
|-----------|-------|---------|
| Bit inverters | 4 | 4 |
| Half-adder chain | 4 | 16 |
| Overflow detect | 1 | 2 |

**Total: 22 neurons, 63 parameters, 4 layers**

## Examples

```
-(+5) = ~(0101) + 1 = 1010 + 1 = 1011 = -5 ✓
-(-3) = ~(1101) + 1 = 0010 + 1 = 0011 = +3 ✓
-(-8) = ~(1000) + 1 = 0111 + 1 = 1000 = -8 (overflow!)
```

## Usage

```python
from safetensors.torch import load_file

w = load_file('model.safetensors')

# All 16 cases verified
# Overflow only when A = -8 (1000)
```

## Files

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

## License

MIT