threshold-carry-generate

Carry generate signal for carry-lookahead adders. Outputs 1 when the bit position will definitely generate a carry, regardless of incoming carry.

Circuit

    a       b
    │       │
    └───┬───┘
        │
        ▼
    ┌───────┐
    │  AND  │
    │ w:1,1 │
    │ b: -2 │
    └───────┘
        │
        ▼
       G(a,b)

Function

generate(a, b) = a AND b

A carry is generated at position i when both inputs are 1, because 1+1=10 in binary always produces a carry.

Truth Table

a	b	G	Meaning
0	0	0	0+0=0, no carry
0	1	0	0+1=1, no carry
1	0	0	1+0=1, no carry
1	1	1	1+1=10, generates carry

Mechanism

The AND gate fires when both inputs contribute, guaranteeing a carry output:

• Weighted sum = a + b
• Bias = -2 requires both inputs to be 1
• Result: outputs 1 only when a=1 AND b=1

Carry-Lookahead Context

In a carry-lookahead adder, each bit position computes two signals:

Signal	Function	Meaning
G (Generate)	a AND b	Will produce carry regardless of Cin
P (Propagate)	a XOR b	Will pass through incoming carry

The carry equation becomes:

C[i+1] = G[i] OR (P[i] AND C[i])

For multi-bit lookahead:

C[4] = G[3] OR (P[3] AND G[2]) OR (P[3] AND P[2] AND G[1]) OR (P[3] AND P[2] AND P[1] AND G[0]) OR (P[3] AND P[2] AND P[1] AND P[0] AND C[0])

Parameters

Weights	[1, 1]
Bias	-2
Inputs	2
Outputs	1
Neurons	1
Layers	1
Parameters	3
Magnitude	4

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def carry_generate(a, b):
    inp = torch.tensor([float(a), float(b)])
    return int((inp @ w['and.weight'].T + w['and.bias'] >= 0).item())

# Examples
print(carry_generate(0, 0))  # 0
print(carry_generate(0, 1))  # 0
print(carry_generate(1, 0))  # 0
print(carry_generate(1, 1))  # 1 (generates carry)

Applications

• Carry-lookahead adders (CLA)
• Parallel prefix adders (Kogge-Stone, Brent-Kung, etc.)
• High-speed ALU design
• Multiplier partial product reduction

Related Circuits

• threshold-carry-propagate: The P signal (a XOR b)
• threshold-carrylookahead4bit: 4-bit CLA using G and P
• threshold-kogge-stone: Parallel prefix adder

Files

threshold-carry-generate/
├── model.safetensors
├── model.py
├── create_safetensors.py
├── config.json
└── README.md

License

MIT