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)
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