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

# threshold-absolutevalue4

Absolute value of 4-bit 2's complement signed integer.

## Function

abs4(a) = |a| where a is interpreted as 4-bit 2's complement (-8 to +7)

## Truth Table

| Input | Signed | |Abs| | Output |
|-------|--------|------|--------|
| 0000 | +0 | 0 | 0000 |
| 0001 | +1 | 1 | 0001 |
| 0010 | +2 | 2 | 0010 |
| 0011 | +3 | 3 | 0011 |
| 0100 | +4 | 4 | 0100 |
| 0101 | +5 | 5 | 0101 |
| 0110 | +6 | 6 | 0110 |
| 0111 | +7 | 7 | 0111 |
| 1000 | -8 | 8 | 1000 |
| 1001 | -7 | 7 | 0111 |
| 1010 | -6 | 6 | 0110 |
| 1011 | -5 | 5 | 0101 |
| 1100 | -4 | 4 | 0100 |
| 1101 | -3 | 3 | 0011 |
| 1110 | -2 | 2 | 0010 |
| 1111 | -1 | 1 | 0001 |

## Architecture

5-layer circuit implementing conditional 2's complement negation:
- For positive (a3=0): output = input
- For negative (a3=1): output = ~input + 1

Key formulas for negative path:
- o0 = a0 (always)
- o1 = ~a1 XOR ~a0
- o2 = ~a2 XOR (~a1 AND ~a0)
- o3 = 1 only for input 1000 (-8)

## Parameters

| | |
|---|---|
| Inputs | 4 |
| Outputs | 4 |
| Neurons | 23 |
| Layers | 5 |
| Parameters | 145 |
| Magnitude | 64 |

## License

MIT