File size: 2,760 Bytes
60f4258 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 |
---
license: mit
tags:
- formal-verification
- coq
- threshold-logic
- neuromorphic
- arithmetic
- adder
---
# tiny-RippleCarry2Bit-verified
Formally verified 2-bit ripple carry adder. Chains two full adders to add two 2-bit numbers with 100% accuracy.
## Architecture
| Component | Value |
|-----------|-------|
| Inputs | 4 (a1, a0, b1, b0) |
| Outputs | 3 (cout, s1, s0) |
| Neurons | 8 (2 full adders × 4 neurons each) |
| Parameters | 24 (2 full adders × 12 params each) |
| Layers | 2 (chained full adders) |
| Activation | Heaviside step |
## Key Properties
- 100% accuracy (16/16 input combinations correct)
- Coq-proven correctness
- Compositional construction from verified full adders
- Produces 3-bit output (sum can be 0-6, requiring 3 bits)
- Compatible with neuromorphic hardware
## Circuit Structure
```
a1 a0 b1 b0
| | | |
| +--+--+ |
| | |
| FA0 (cin=0)
| | |
| s0 c0
| | |
+--+--+-----+
|
FA1
|
s1 c1
```
First full adder adds least significant bits (a0 + b0 + 0), producing sum bit s0 and carry c0. Second full adder adds most significant bits with the carry (a1 + b1 + c0), producing s1 and final carry cout.
## Usage
```python
import torch
from safetensors.torch import load_file
weights = load_file('ripplecarry2bit.safetensors')
def full_adder_sim(a, b, cin):
sum_out = a ^ b ^ cin
carry_out = (a & b) | (cin & (a ^ b))
return sum_out, carry_out
def ripple_carry_2bit(a1, a0, b1, b0):
s0, c0 = full_adder_sim(a0, b0, 0)
s1, cout = full_adder_sim(a1, b1, c0)
return cout, s1, s0
# Test
print(ripple_carry_2bit(1, 1, 1, 0)) # 3 + 2 = 5 -> (1, 0, 1)
print(ripple_carry_2bit(1, 0, 1, 0)) # 2 + 2 = 4 -> (1, 0, 0)
print(ripple_carry_2bit(0, 1, 0, 1)) # 1 + 1 = 2 -> (0, 1, 0)
```
## Verification
**Coq Theorem**:
```coq
Theorem ripple_carry_2bit_correct : forall a1 a0 b1 b0,
ripple_carry_2bit a1 a0 b1 b0 = ripple_carry_2bit_spec a1 a0 b1 b0.
```
Proven axiom-free via exhaustive case analysis on all 16 input combinations.
Full proof: [coq-circuits/Arithmetic/RippleCarry2Bit.v](https://github.com/CharlesCNorton/coq-circuits/blob/main/coq/Arithmetic/RippleCarry2Bit.v)
## Properties
- **Commutative**: Adding A + B equals B + A
- **Identity**: Adding 0 preserves the value
- **Compositional**: Built from two verified FullAdder circuits
## Citation
```bibtex
@software{tiny_ripplecarry2bit_verified_2025,
title={tiny-RippleCarry2Bit-verified: Formally Verified 2-Bit Ripple Carry Adder},
author={Norton, Charles},
url={https://huggingface.co/phanerozoic/tiny-RippleCarry2Bit-verified},
year={2025}
}
```
|