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

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