threshold-signbit4

Extract sign bit (MSB) of 4-bit number.

Function

signbit4(a3, a2, a1, a0) = a3

In 2's complement representation:

• Output 0: non-negative (0 to 7)
• Output 1: negative (-8 to -1)

Truth Table

a3	a2	a1	a0	unsigned	signed	signbit
0	0	0	0	0	0	0
0	1	1	1	7	+7	0
1	0	0	0	8	-8	1
1	1	1	1	15	-1	1

Architecture

Single neuron extracting MSB:

• Weights: [1, 0, 0, 0]
• Bias: -1

Fires when: a3 - 1 >= 0, i.e., a3 >= 1

Parameters

Inputs	4
Outputs	1
Neurons	1
Layers	1
Parameters	5
Magnitude	2

Usage

from safetensors.torch import load_file
import torch

w = load_file('model.safetensors')

def signbit4(a3, a2, a1, a0):
    inp = torch.tensor([float(a3), float(a2), float(a1), float(a0)])
    return int((inp @ w['neuron.weight'].T + w['neuron.bias'] >= 0).item())

print(signbit4(0, 1, 1, 1))  # 0 (value = +7)
print(signbit4(1, 0, 0, 0))  # 1 (value = -8)

License

MIT