threshold-bcd-adder

BCD (Binary-Coded Decimal) single-digit adder as threshold circuit. Adds two decimal digits (0-9) with carry.

Circuit

A[3:0] ──┐  (BCD digit 0-9)
B[3:0] ──┼──► BCD Adder ──┬──► S[3:0]  (BCD digit 0-9)
Cin    ──┘                └──► Cout    (decimal carry)

Algorithm

1. Binary add: Z = A + B + Cin  (4-bit result + carry)
2. Detect overflow: Z > 9 OR binary carry
3. If overflow: add 6 (0110) for correction
4. Decimal carry = overflow detected

Why Add 6?

BCD uses only values 0-9. When binary sum exceeds 9:

• 10 (1010) + 6 = 16 (10000) → 0 with carry
• 11 (1011) + 6 = 17 (10001) → 1 with carry
• etc.

Adding 6 skips the invalid codes A-F (10-15).

Truth Table (examples)

A	B	Cin	S	Cout
5	3	0	8	0
5	5	0	0	1
9	9	0	8	1
9	9	1	9	1

Architecture

Stage	Component	Neurons
Binary add	4 Full Adders	28
Detect >9	AND, OR gates	4
Correction	2 Half Adders + XOR	11

Total: 43 neurons, 133 parameters, 5 layers

Applications

• Decimal arithmetic in calculators
• Financial calculations requiring exact decimal
• BCD-based displays (7-segment)
• Legacy systems using packed BCD

Usage

from safetensors.torch import load_file

w = load_file('model.safetensors')

# Valid inputs: A, B in range 0-9
# All 200 test cases verified (10 × 10 × 2)

Files

threshold-bcd-adder/
├── model.safetensors
├── create_safetensors.py
├── config.json
└── README.md

License

MIT