Theory 

1. BCD (Binary Coded Decimal) represents decimal digits (0–9) in pure 4-bit binary.

2. Excess-3 was obtained by adding 3 (0011) to BCD.

3. So , to convert back:
   BCD=Excess-3−0011

Conversion Rule (Excess-3 → BCD)

1. Take the Excess-3 input.

2. Subtract 0011 (3 in binary).

3. Result = BCD code.

Truth Table 

K Map  

Boolean expression 

Logic Circuit