threshold-decrementer4bit

4-bit decrementer. Subtracts 1 from input (modulo 16).

Function

decrementer4bit(a3, a2, a1, a0) = (input - 1) mod 16

Truth Table (selected rows)

Input	Decimal	Output	Decimal
0000	0	1111	15
0001	1	0000	0
1000	8	0111	7
1111	15	1110	14

Architecture

y0 = NOT(a0)
y1 = XNOR(a1, a0) = a1 XOR NOT(a0)
y2 = a2 XOR NOR(a1, a0)
y3 = a3 XOR NOR(a2, a1, a0)

Borrow propagation: flip each bit if all lower bits are 0.

Layer 1: Compute NOT(a0), borrow signals (b1=NOR, b2=NOR3), XNOR component Layer 2: Complete XNOR for y1, XOR components for y2 and y3 Layer 3: Final AND gates for y2 and y3

Parameters

Inputs	4
Outputs	4
Neurons	11
Layers	3
Parameters	56
Magnitude	33

Usage

from safetensors.torch import load_file
# See model.py for full implementation

# 8 - 1 = 7
# decrementer4(1, 0, 0, 0) = [0, 1, 1, 1]

# 0 - 1 = 15 (wraps)
# decrementer4(0, 0, 0, 0) = [1, 1, 1, 1]

License

MIT